http://wiki.math.uwaterloo.ca/statwiki/api.php?action=feedcontributions&user=Jcllau&feedformat=atomstatwiki - User contributions [US]2022-11-29T07:41:16ZUser contributionsMediaWiki 1.28.3http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Surround_Vehicle_Motion_Prediction&diff=49418Surround Vehicle Motion Prediction2020-12-06T17:10:32Z<p>Jcllau: /* Critiques */</p>
<hr />
<div>DROCC: '''Surround Vehicle Motion Prediction Using LSTM-RNN for Motion Planning of Autonomous Vehicles at Multi-Lane Turn Intersections'''<br />
== Presented by == <br />
Mushi Wang, Siyuan Qiu, Yan Yu<br />
<br />
== Introduction ==<br />
<br />
This paper presents a surrounding vehicle motion prediction algorithm for multi-lane turn intersections using a Long Short-Term Memory (LSTM)-based Recurrent Neural Network (RNN). More specifically, it focused on the improvement of in-lane target recognition and achieving human-like acceleration decisions at multi-lane turn intersections by introducing the learning-based target motion predictor and prediction-based motion predictor. A data-driven approach for predicting the trajectory and velocity of surrounding vehicles on urban roads at multi-lane turn intersections was described. LSTM architecture, a specific kind of RNN capable of learning long-term dependencies, is designed to manage complex vehicle motions in multi-lane turn intersections. The results show that the forecaster improves the recognition time of the leading vehicle and contributes to the improvement of prediction ability.<br />
<br />
== Previous Work ==<br />
The autonomous vehicle trajectory approaches previously used motion models like Constant Velocity and Constant Acceleration. These models are linear and are only able to handle straight motions. There are curvilinear models such as Constant Turn Rate and Velocity and Constant Turn Rate and Acceleration which handle rotations and more complex motions. Together with these models, Kalman Filter is used to predicting the vehicle trajectory. Kalman filtering is a common technique used in sensor fusion for state estimation that allows the vehicle's state to be predicted while taking into account the uncertainty associated with inputs and measurements. However, the performance of the Kalman Filter in predicting multi-step problems is not that good. Recurrent Neural Network performs significantly better than it. <br />
<br />
There are 3 main challenges to achieving fully autonomous driving on urban roads, which are scene awareness, inferring other drivers’ intentions, and predicting their future motions. Researchers are developing prediction algorithms that can simulate a driver’s intuition to improve safety when autonomous vehicles and human drivers drive together. To predict driver behavior on an urban road, there are 3 categories for the motion prediction model: (1) physics-based; (2) maneuver-based; and (3) interaction-aware. Physics-based models are simple and direct, which only consider the states of prediction vehicles kinematically. The advantage is that it has minimal computational burden among the three types. However, it is impossible to consider the interactions between vehicles. Maneuver-based models consider the driver’s intention and classified them. By predicting the driver maneuver, the future trajectory can be predicted. Identifying similar behaviors in driving is able to infer different drivers' intentions which are stated to improve the prediction accuracy. However, it still an assistant to improve physics-based models. <br />
<br />
Recurrent Neural Network (RNN) is a type of approach proposed to infer driver intention in this paper. Interaction-aware models can reflect interactions between surrounding vehicles, and predict future motions of detected vehicles simultaneously as a scene. While the prediction algorithm is more complex in computation which is often used in offline simulations. As Schulz et al. indicate, interaction models are very difficult to create as "predicting complete trajectories at once is challenging, as one needs to account for multiple hypotheses and long-term interactions between multiple agents" [6].<br />
<br />
== Motivation == <br />
Research results indicate that little research has been dedicated on predicting the trajectory of intersections. Moreover, public data sets for analyzing driver behaviour at intersections are not enough, and these data sets are not easy to collect. A model is needed to predict the various movements of the target around a multi-lane turning intersection. It is very necessary to design a motion predictor that can be used for real-time traffic.<br />
<br />
<center><br />
[[ File:intersection.png |300px]]<br />
</center><br />
<br />
== Framework == <br />
The LSTM-RNN-based motion predictor comprises three parts: (1) a data encoder; (2) an LSTM-based RNN; and (3) a data decoder depicts the architecture of the surrounding target trajectory predictor. The proposed architecture uses a perception algorithm to estimate the state of surrounding vehicles, which relies on six scanners. The output predicts the state of the surrounding vehicles and is used to determine the expected longitudinal acceleration in the actual traffic at the intersection. The following image gives a visual representation of the model.<br />
<br />
<center>[[Image:Figure1_Yan.png|800px|]]</center><br />
<br />
== LSTM-RNN based motion predictor == <br />
<br />
=== Sensor Outputs ===<br />
<br />
The input of the target perceptions is from the output of the sensors. The data collected in this article uses 6 different sensors with feature fusion to detect traffic in the range up to 100m: 1) LiDAR system outputs: Relative position, heading, velocity, and box size in local coordinates; 2) Around-View Monitoring (AVM) and 3)GPS outputs: acquire lanes, road marker, global position; 4) Gateway engine outputs: precise global position in urban road environment; 5) Micro-Autobox II and 6) a MDPS are used to control and actuate the subject. All data are stored in an industrial PC.<br />
<br />
=== Data ===<br />
Multi-lane turn intersections are the target roads in this paper. The dataset was collected using a human driven Autonomous Vehicle(AV) that was equipped with sensors to track motion the vehicle's surroundings. In addition the motion sensors they used a front camera, Around-View-Monitor and GPS to acquire the lanes, road markers and global position. The data was collected in the urban roads of Gwanak-gu, Seoul, South Korea. The training model is generated from 484 tracks collected when driving through intersections in real traffic. The previous and subsequent states of a vehicle at a particular time can be extracted. After post-processing, the collected data, a total of 16,660 data samples were generated, including 11,662 training data samples, and 4,998 evaluation data samples.<br />
<br />
=== Motion predictor ===<br />
This article proposes a data-driven method to predict the future movement of surrounding vehicles based on their previous movement, which is the sequential previous motion. The motion predictor based on the LSTM-RNN architecture in this work only uses information collected from sensors on autonomous vehicles, as shown in the figure below. The contribution of the network architecture of this study is that the future state of the target vehicle is used as the input feature for predicting the field of view. <br />
<br />
<br />
<center>[[Image:Figure7b_Yan.png|500px|]]</center><br />
<br />
<br />
==== Network architecture ==== <br />
A RNN is an artificial neural network that is suitable for use with sequential data because it has recurrent connections on its hidden nodes and thus, can retain its state or memory while processing the next input or sequence of inputs. For this reason, RNNs can be used to analyze time-series data where the pattern of the data depends on the time flow. This is an impossible task for traditional artificial neural networks, which assume the inputs are independent of one another. RNNs can also contain feedback loops that allow activations to flow alternately in the loop. <br />
<br />
In line with traditional neural networks, RNNs still suffer from the problem of vanishing gradients. An LSTM avoids this by making errors flow backward without a limit on the number of virtual layers. This property prevents errors from increasing or declining over time, which can make the network train improperly. The figure below shows the various layers of the LSTM-RNN and the number of units in each layer. This structure is determined by comparing the accuracy of 72 RNNs, which consist of a combination of four input sets and 18 network configurations.<br />
<br />
<center>[[Image:Figure8_Yan.png|800px|]]</center><br />
<br />
==== Input and output features ==== <br />
In order to apply the motion predictor to the AV in motion, the speed of the data collection vehicle is added to the input sequence. The input sequence consists of relative X/Y position, relative heading angle, speed of surrounding target vehicles, and speed of data collection vehicles. The output sequence is the same as the input sequence, such as relative position, heading, and speed.<br />
<br />
==== Encoder and decoder ==== <br />
In this study, the authors introduced an encoder and decoder that process the input from the sensor and the output from the RNN, respectively. The encoder normalizes each component of the input data to rescale the data to mean 0 and standard deviation 1, while the decoder denormalizes the output data to use the same parameters as in the encoder to scale it back to the actual unit. <br />
==== Sequence length ==== <br />
The sequence length of RNN input and output is another important factor to improve prediction performance. In this study, 5, 10, 15, 20, 25, and 30 steps of 100 millisecond sampling times were compared, and 15 steps showed relatively accurate results, even among candidates The observation time is very short.<br />
<br />
== Motion planning based on surrounding vehicle motion prediction == <br />
In daily driving, experienced drivers will predict possible risks based on observations of surrounding vehicles, and ensure safety by changing behaviors before the risks occur. In order to achieve a human-like motion plan, based on the model predictive control (MPC) method, a prediction-based motion planner for autonomous vehicles is designed, which takes into account the driver’s future behavior. The cost function of the motion planner is determined as follows:<br />
\begin{equation*}<br />
\begin{split}<br />
J = & \sum_{k=1}^{N_p} (x(k|t) - x_{ref}(k|t)^T) Q(x(k|t) - x_{ref}(k|t)) +\\<br />
& R \sum_{k=0}^{N_p-1} u(k|t)^2 + R_{\Delta \mu}\sum_{k=0}^{N_p-2} (u(k+1|t) - u(k|t))^2 <br />
\end{split}<br />
\end{equation*}<br />
where <math>k</math> and <math>t</math> are the prediction step index and time index, respectively; <math>x(k|t)</math> and <math>x_{ref} (k|t)</math> are the states and reference of the MPC problem, respectively; <math>x(k|t)</math> is composed of travel distance px and longitudinal velocity vx; <math>x_{ref} (k|t)</math> consists of reference travel distance <math>p_{x,ref}</math> and reference longitudinal velocity <math>v_{x,ref}</math> ; <math>u(k|t)</math> is the control input, which is the longitudinal acceleration command; <math>N_p</math> is the prediction horizon; and Q, R, and <math>R_{\Delta \mu}</math> are the weight matrices for states, input, and input derivative, respectively, and these weight matrices were tuned to obtain control inputs from the proposed controller that were as similar as possible to those of human-driven vehicles. <br />
The constraints of the control input are defined as follows:<br />
\begin{equation*}<br />
\begin{split}<br />
&\mu_{min} \leq \mu(k|t) \leq \mu_{max} \\<br />
&||\mu(k+1|t) - \mu(k|t)|| \leq S<br />
\end{split}<br />
\end{equation*}<br />
Where <math>u_{min}</math>, <math>u_{max}</math>and S are the minimum/maximum control input and maximum slew rate of input respectively.<br />
<br />
Determine the position and speed boundary based on the predicted state:<br />
\begin{equation*}<br />
\begin{split}<br />
& p_{x,max}(k|t) = p_{x,tar}(k|t) - c_{des}(k|t) \quad p_{x,min}(k|t) = 0 \\<br />
& v_{x,max}(k|t) = min(v_{x,ret}(k|t), v_{x,limit}) \quad v_{x,min}(k|t) = 0<br />
\end{split}<br />
\end{equation*}<br />
Where <math>v_{x, limit}</math> are the speed limits of the target vehicle.<br />
<br />
== Prediction performance analysis and application to motion planning ==<br />
=== Accuracy analysis ===<br />
The proposed algorithm was compared with the results from three base algorithms, a path-following model with <br />
constant velocity, a path-following model with traffic flow and a CTRV model.<br />
<br />
We compare those algorithms according to four sorts of errors, The <math>x</math> position error <math>e_{x,T_p}</math>, <br />
<math>y</math> position error <math>e_{y,T_p}</math>, heading error <math>e_{\theta,T_p}</math>, and velocity error <math>e_{v,T_p}</math> where <math>T_p</math> denotes time <math>p</math>. These four errors are defined as follows:<br />
<br />
\begin{equation*}<br />
\begin{split}<br />
e_{x,Tp}=& p_{x,Tp} -\hat {p}_{x,Tp}\\ <br />
e_{y,Tp}=& p_{y,Tp} -\hat {p}_{y,Tp}\\ <br />
e_{\theta,Tp}=& \theta _{Tp} -\hat {\theta }_{Tp}\\ <br />
e_{v,Tp}=& v_{Tp} -\hat {v}_{Tp}<br />
\end{split}<br />
\end{equation*}<br />
<center>[[Image:Figure10.1_YanYu.png|500px|]]</center><br />
<br />
The proposed model shows significantly fewer prediction errors compare to the based algorithms in terms of mean, <br />
standard deviation(STD), and root mean square error(RMSE). Meanwhile, the proposed model exhibits a bell-shaped <br />
curve with a close to zero mean, which indicates that the proposed algorithm's prediction of human divers' <br />
intensions are relatively precise. On the other hand, <math>e_{x,T_p}</math>, <math>e_{y,T_p}</math>, <math>e_{v,T_p}</math> are bounded within <br />
reasonable levels. For instant, the three-sigma range of <math>e_{y,T_p}</math> is within the width of a lane. Therefore, <br />
the proposed algorithm can be precise and maintain safety simultaneously.<br />
<br />
=== Motion planning application ===<br />
==== Case study of a multi-lane left turn scenario ====<br />
The proposed method mimics a human driver better, by simulating a human driver's decision-making process. <br />
In a multi-lane left turn scenario, the proposed algorithm correctly predicted the trajectory of a target <br />
the vehicle, even when the target vehicle was not following the intersection guideline.<br />
<br />
==== Statistical analysis of motion planning application results ====<br />
The data is analyzed from two perspectives, the time to recognize the in-lane target and the similarity to <br />
human driver commands. In most of cases, the proposed algorithm detects the in-line target no late than based <br />
algorithm. In addition, the proposed algorithm only recognized cases later than the base algorithm did when <br />
the surrounding target vehicles first appeared beyond the sensors’ region of interest boundaries. This means <br />
that these cases took place sufficiently beyond the safety distance, and had little influence on determining <br />
the behaviour of the subject vehicle.<br />
<br />
<center>[[Image:Figure11_YanYu.png|500px|]]</center><br />
<br />
In order to compare the similarities between the results form the proposed algorithm and human driving decisions, <br />
this article introduced another type of error, acceleration error <math>a_{x, error} = a_{x, human} - a_{x, cmd}</math>. where <math>a_{x, human}</math><br />
and <math>a_{x, cmd}</math> are the human driver’s acceleration history and the command from the proposed algorithm, <br />
respectively. The proposed algorithm showed more similar results to human drivers’ decisions than the base <br />
algorithm. <math>91.97\%</math> of the acceleration error lies in the region <math>\pm 1 m/s^2</math>. Moreover, the base algorithm <br />
possesses a limited ability to respond to different in-lane target behaviours in traffic flow. Hence, the proposed <br />
model is efficient and safe.<br />
<br />
== Conclusion ==<br />
A surrounding vehicle motion predictor based on an LSTM-RNN at multi-lane turn intersections was developed and its application in an autonomous vehicle was evaluated. The model was trained by using the data captured on the urban road in Seoul in MPC. The evaluation results showed precise prediction accuracy and so the algorithm is safe to be applied on an autonomous vehicle. Also, the comparison with the other three base algorithms (CV/Path, V_flow/Path, and CTRV) revealed the superiority of the proposed algorithm. The evaluation results showed precise prediction accuracy. In addition, the time-to-recognize in-lane targets within the intersection improved significantly over the performance of the base algorithms. The proposed algorithm was compared with human driving data, and it showed similar longitudinal acceleration. The motion predictor can be applied to path planners when AVs travel in unconstructed environments, such as multi-lane turn intersections.<br />
<br />
== Future works ==<br />
This paper has identified several venues for future research, which include:<br />
<br />
1.Developing trajectory prediction algorithms using other machine learning algorithms, such as attention-aware neural networks.<br />
<br />
2.Applying the machine learning-based approach to infer lane change intention at motorways and main roads of urban environments.<br />
<br />
3.Extending the target road of the trajectory predictor, such as roundabouts or uncontrolled intersections, to infer yield intention.<br />
<br />
4.Learning the behavior of surrounding vehicles in real time while automated vehicles drive with real traffic.<br />
<br />
== Critiques ==<br />
The literature review is not sufficient. It should focus more on LSTM, RNN, and the study in different types of roads. Why the LSTM-RNN is used, and the background of the method is not stated clearly. There is a lack of concept so that it is difficult to distinguish between LSTM-RNN based motion predictor and motion planning.<br />
<br />
This is an interesting topic to discuss. This is a major topic for some famous vehicle companies such as Tesla, which now already has a good service called Autopilot to give self-driving and Motion Prediction. This summary can include more diagrams in architecture in the model to give readers a whole view of how the model looks like. Since it is using LSTM-RNN, include some pictures of the LSTM-RNN will be great. I think it will be interesting to discuss more applications by using this method, such as Airplane, boats.<br />
<br />
Autonomous driving is a very hot topic, and training the model with LSTM-RNN is also a meaningful topic to discuss. By the way, it would be an interesting approach to compare the performance of different algorithms or some other traditional motion planning algorithms like KF.<br />
<br />
There are some papers that discussed the accuracy of different models in vehicle predictions, such as Deep Kinematic Models for Kinematically Feasible Vehicle Trajectory Predictions[https://arxiv.org/pdf/1908.00219.pdf.] The LSTM didn't show good performance. They increased the accuracy by combing LSTM with an unconstrained model(UM) by adding an additional LSTM layer of size 128 that is used to recursively output positions instead of simultaneously outputting positions for all horizons.<br />
<br />
It may be better to provide the results of experiments to support the efficiency of LSTM-RNN, talk about the prediction of training and test sets, and compared it with other autonomous driving systems that exist in the world.<br />
<br />
The topic of surround vehicle motion prediction is analogous to the topic of autonomous vehicles. An example of an application of these frameworks would be the transportation services industry. Many companies, such as Lyft and Uber, have started testing their own commercial autonomous vehicles.<br />
<br />
It would be really helpful if some visualization or data summary can be provided to understand the content, such as the track of the car movement.<br />
<br />
The model should have been tested in other regions besides just Seoul, as driving behaviors can vary drastically from region to region.<br />
<br />
Understandably, a supervised learning problem should be evaluated on some test dataset. However, supervised learning techniques are inherently ill-suited for general planning problems. The test dataset was obtained from human driving data which is known to be extremely noisy as well as unpredictable when it comes to motion planning. It would be crucial to determine the successes of this paper based on the state-of-the-art reinforcement learning techniques.<br />
<br />
It would be better if the authors compared their method against other SOTA methods. Also one of the reasons motion planning is done using interpretable methods rather than black boxes (such as this model) is because it is hard to see where things go wrong and fix problems with the black box when they occur - this is something the authors should have also discussed.<br />
<br />
A future area of study is to combine other source of information such as signals from Lidar or car side cameras to make a better prediction model.<br />
<br />
It might be interesting and helpful to conduct some training and testing under different weather/environmental conditions, as it could provide more generalization to real-life driving scenarios. For example, foggy weather and evening (low light) conditions might affect the performance of sensors, and rainy weather might require a longer braking distance.<br />
<br />
This paper proposes an interesting, novel model prediction algorithm, using LSTM_RNN. However, since motion prediction in autonomous driving has great real-life impacts, I do believe that the evaluations of the algorithm should be more thorough. For example, more traditional motion planning algorithms such as multi-modal estimation and Kalman filters should be used as benchmarks. Moreover, the experiment results are based on Korean driving conditions only. Eastern and Western drivers can have very different driving patterns, so that should be addressed in the discussion section of the paper as well.<br />
<br />
The paper mentions that in the future, this research plans to learn the real life behaviour of automated vehicles. Seeing a possible improvement in road safety due to this research will be very interesting.<br />
<br />
This predictor is also possible to be applied in the traffic control system.<br />
<br />
This prediction model should consider various conditions that could happen in an intersection. However, normal prediction may not work when there is a traffic jam or in some crowded time periods like rush hours.<br />
<br />
It would be better that the author could provide more comparison between the LSTN-RNN algorithm and other traditional algorithm such as RNN or just LSTM.<br />
<br />
The paper has really good results for what they aimed to achieve. However for the future work it would also be nice to have various climates/weathers to be included in the Seoul dataset. I think it's also important to consider it as different climates/weather (such as snowy roads, or rain) would introduce more noisier data (camera's image processing) and the human drivers behaviour would change as well to adapt to the new environment.<br />
<br />
It would be good to have a future work section to discusses shortage of current algorithms and the possible improvement.<br />
<br />
The summary explains the whole process well, but is missing the small details among the steps. It would be better to explain concepts such as RNN, modelling procedure for first time users.<br />
<br />
This paper presents a nice method, but does not seem particularly well developed. I would have liked to see some more ablations on this particular choice of RNN, as there are more efficient variants such as GRU which show similar performance in other tasks while being more amenable to real-time inference. Furthermore, the multi-model aspect seems slightly ad-hoc, it would have been nice to see a more rigorous formulation similar to seen in some recent work by Zeng et al. from Uber ATG: https://arxiv.org/pdf/2008.06041.pdf.<br />
<br />
The data used for this paper contains driver information exclusively to the urban roads of Gwanak-gu Seoul, hence the data may contain an inherited bias as drivers around the rest of the country, let alone the rest of the world, will have different habits based on different environments. It would be interesting to see if this model can be applied to other cities around the world and exhibit similar results or would there be a need to tune it based off geographic location.<br />
<br />
Since the data is based on urban roads, It would be better to include the details on performance of the model on high traffic area vs low traffic urban area. It would also be interesting to see the performance of the model with many pedestrians.<br />
<br />
While it would be nice to read more on why the authors chose LSTM-RNN, the paper exhibits a potential way to improve autonomous vehicle performance. It would be interesting to see how an army of robots would behave when this paper's method is applied in robotics, since robots' motions also follow a trajectory.<br />
<br />
== Reference ==<br />
[1] E. Choi, Crash Factors in Intersection-Related Crashes: An On-Scene Perspective (No. Dot HS 811 366), U.S. DOT Nat. Highway Traffic Safety Admin., Washington, DC, USA, 2010.<br />
<br />
[2] D. J. Phillips, T. A. Wheeler, and M. J. Kochenderfer, “Generalizable intention prediction of human drivers at intersections,” in Proc. IEEE Intell. Veh. Symp. (IV), Los Angeles, CA, USA, 2017, pp. 1665–1670.<br />
<br />
[3] B. Kim, C. M. Kang, J. Kim, S. H. Lee, C. C. Chung, and J. W. Choi, “Probabilistic vehicle trajectory prediction over occupancy grid map via recurrent neural network,” in Proc. IEEE 20th Int. Conf. Intell. Transp. Syst. (ITSC), Yokohama, Japan, 2017, pp. 399–404.<br />
<br />
[4] E. Strigel, D. Meissner, F. Seeliger, B. Wilking, and K. Dietmayer, “The Ko-PER intersection laserscanner and video dataset,” in Proc. 17th Int. IEEE Conf. Intell. Transp. Syst. (ITSC), Qingdao, China, 2014, pp. 1900–1901.<br />
<br />
[5] Henggang Cui, Thi Nguyen, Fang-Chieh Chou, Tsung-Han Lin, Jeff Schneider, David Bradley, Nemanja Djuric: “Deep Kinematic Models for Kinematically Feasible Vehicle Trajectory Predictions”, 2019; [http://arxiv.org/abs/1908.00219 arXiv:1908.00219].<br />
<br />
[6]Schulz, Jens & Hubmann, Constantin & Morin, Nikolai & Löchner, Julian & Burschka, Darius. (2019). Learning Interaction-Aware Probabilistic Driver Behavior Models from Urban Scenarios. 10.1109/IVS.2019.8814080.</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Music_Recommender_System_Based_using_CRNN&diff=49408Music Recommender System Based using CRNN2020-12-06T16:40:50Z<p>Jcllau: /* Critiques/ Insights: */</p>
<hr />
<div>==Introduction and Objective:==<br />
<br />
In the digital era of music streaming, companies, such as Spotify and Pandora, are faced with the following challenge: can they provide users with relevant and personalized music recommendations amidst the ever-growing abundance of music and user data?<br />
<br />
The objective of this paper is to implement a personalized music recommender system that takes user listening history as input and continually finds new music that captures individual user preferences.<br />
<br />
This paper argues that a music recommendation system should vary from the general recommendation system used in practice since it should combine music feature recognition and audio processing technologies to extract music features, and combine them with data on user preferences.<br />
<br />
The authors of this paper took a content-based music approach to build the recommendation system - specifically, comparing the similarity of features based on the audio signal.<br />
<br />
The following two-method approach for building the recommendation system was followed:<br />
#Make recommendations including genre information extracted from classification algorithms.<br />
#Make recommendations without genre information.<br />
<br />
The authors used convolutional recurrent neural networks (CRNN), which is a combination of convolutional neural networks (CNN) and recurrent neural network(RNN), as their main classification model.<br />
<br />
==Methods and Techniques:==<br />
Generally, a music recommender can be divided into three main parts: (i) users, (ii) items, and (iii) user-item matching algorithms. Firstly, a model for a user's music taste is generated based on their profiles. Secondly, item profiling based on editorial, cultural, and acoustic metadata is exploited to increase listener satisfaction. Thirdly, a matching algorithm is employed to recommend personalized music to the listener. Two main approaches are currently available;<br />
<br />
1. Collaborative filtering<br />
<br />
It is based on users' historical listening data and depends on user ratings. Nearest neighbour is the standard method used for collaborative filtering and can be broken into two classes of methods: (i) user-based neighbourhood methods and (ii) item-based neighbourhood methods. <br />
<br />
User-based neighbourhood methods calculate the similarity between the target user and other users, and selects the k most similar. A weighted average of the most similar users' song ratings is then computed to predict how the target user would rate those songs. Songs that have a high predicted rating are then recommended to the user. In contrast, methods that use item-based neighbourhoods calculate similarities between songs that the target user has rated well and songs they have not listened to in order to recommend songs.<br />
<br />
That being said, collaborative filtering faces many challenges. For example, given that each user sees only a small portion of all music libraries, sparsity and scalability become an issue. However, this can be dealt with using matrix factorization. A more difficult challenge to overcome is the fact that users often don't rate songs when they are listening to music. <br />
<br />
2. Content-based filtering<br />
<br />
Content based recommendation systems base their recommendations on the similarity of an items features and features that the user has enjoyed. It has two-steps; (i) Extract audio content features and (ii) predict user preferences.<br />
<br />
In this work, the authors take a content-based approach, as they compare the similarity of audio signal features to make recommendations. To classify music, the original music’s audio signal is converted into a spectrogram image. Using the image and the Short Time Fourier Transform (STFT), we convert the data into the Mel scale which is used in the CNN and CRNN models. <br />
=== Mel Scale: === <br />
The scale of pitches that are heard by listeners, which translates to equal pitch increments.<br />
<br />
[[File:Mel.png|frame|none|Mel Scale on Spectrogram]]<br />
<br />
=== Short Time Fourier Transform (STFT): ===<br />
The transformation that determines the sinusoidal frequency of the audio, with a Hanning smoothing function. In the continuous case this is written as: <math>\mathbf{STFT}\{x(t)\}(\tau,\omega) \equiv X(\tau, \omega) = \int_{-\infty}^{\infty} x(t) w(t-\tau) e^{-i \omega t} \, d t </math><br />
<br />
where: <math>w(\tau)</math> is the Hanning smoothing function. The STFT is applied over a specified window length at a certain time allowing the frequency to represented for that given window rather than the entire signal as a typical Fourier Transform would.<br />
<br />
=== Convolutional Neural Network (CNN): ===<br />
A Convolutional Neural Network is a Neural Network that uses convolution in place of matrix multiplication for some layer calculations. By training the data, weights for inputs are updated to find the most significant data relevant to classification. These convolutional layers gather small groups of data with kernels and try to find patterns that can help find features in the overall data. The features are then used for classification. Padding is another technique used to extend the pixels on the edge of the original image to allow the kernel to more accurately capture the borderline pixels. Padding is also used if one wishes the convolved output image to have a certain size. The image on the left represents the mathematical expression of a convolution operation, while the right image demonstrates an application of a kernel on the data.<br />
<br />
[[File:Convolution.png|thumb|400px|left|Convolution Operation]]<br />
[[File:PaddingKernels.png|thumb|400px|center|Example of Padding (white 0s) and Kernels (blue square)]]<br />
<br />
=== Convolutional Recurrent Neural Network (CRNN): === <br />
The CRNN is similar to the architecture of a CNN, but with the addition of a GRU, which is a Recurrent Neural Network (RNN). An RNN is used to treat sequential data, by reusing the activation function of previous nodes to update the output. A Gated Recurrent Unit (GRU) is used to store more long-term memory and will help train the early hidden layers. GRUs can be thought of as LSTMs but with a forget gate, and has fewer parameters than an LSTM. These gates are used to determine how much information from the past should be passed along onto the future. They are originally aimed to prevent the vanishing gradient problem, since deeper networks will result in smaller and smaller gradients at each layer. The GRU can choose to copy over all the information in the past, thus eliminating the risk of vanishing gradients.<br />
<br />
[[File:GRU441.png|thumb|400px|left|Gated Recurrent Unit (GRU)]]<br />
[[File:Recurrent441.png|thumb|400px|center|Diagram of General Recurrent Neural Network]]<br />
<br />
==Data Screening:==<br />
<br />
The authors of this paper used a publicly available music dataset made up of 25,000 30-second songs from the Free Music Archives which contains 16 different genres. The data is cleaned up by removing low audio quality songs, wrongly labelled genres and those that have multiple genres. To ensure a balanced dataset, only 1000 songs each from the genres of classical, electronic, folk, hip-hop, instrumental, jazz and rock were used in the final model. <br />
<br />
[[File:Data441.png|thumb|200px|none|Data sorted by music genre]]<br />
<br />
==Implementation:==<br />
<br />
=== Modeling Neural Networks ===<br />
<br />
As noted previously, both CNNs and CRNNs were used to model the data. The advantage of CRNNs is that they are able to model time sequence patterns in addition to frequency features from the spectrogram, allowing for greater identification of important features. Furthermore, feature vectors produced before the classification stage could be used to improve accuracy. <br />
<br />
In implementing the neural networks, the Mel-spectrogram data was split up into training, validation, and test sets at a ratio of 8:1:1 respectively and labelled via one-hot encoding. This made it possible for the categorical data to be labelled correctly for binary classification. As opposed to classical stochastic gradient descent, the authors opted to use binary classier and ADAM optimization to update weights in the training phase, and parameters of <math>\alpha = 0.001, \beta_1 = 0.9, \beta_2 = 0.999</math>. Binary cross-entropy was used as the loss function. <br />
Input spectrogram image are 96x1366. In both the CNN and CRNN models, the data was trained over 100 epochs and batch size of 50 (limited computing power) with a binary cross-entropy loss function. Notable model specific details are below:<br />
<br />
'''CNN'''<br />
* Five convolutional layers with 3x3 kernel, stride 1, padding, batch normalization, and ReLU activation<br />
* Max pooling layers <br />
* The sigmoid function was used as the output layer<br />
<br />
'''CRNN'''<br />
* Four convolutional layers with 3x3 kernel (which construct a 2D temporal pattern - two layers of RNNs with Gated Recurrent Units), stride 1, padding, batch normalization, ReLU activation, and dropout rate 0.1<br />
* Feature maps are N x1x15 (N = number of features maps, 68 feature maps in this case) is used for RNNs.<br />
* 4 Max pooling layers for four convolutional layers with kernel ((2x2)-(3x3)-(4x4)-(4x4)) and same stride<br />
* The sigmoid function was used as the output layer<br />
<br />
The CNN and CRNN architecture is also given in the charts below.<br />
<br />
[[File:CNN441.png|thumb|800px|none|Implementation of CNN Model]]<br />
[[File:CRNN441.png|thumb|800px|none|Implementation of CRNN Model]]<br />
<br />
=== Music Recommendation System ===<br />
<br />
The recommendation system is computed by the cosine similarity of the extraction features from the neural network. Each genre will have a song act as a centre point for each class. The final inputs of the trained neural networks will be the feature variables. The featured variables will be used in the cosine similarity to find the best recommendations. <br />
<br />
The values are between [-1,1], where larger values are songs that have similar features. When the user inputs five songs, those songs become the new inputs in the neural networks and the features are used by the cosine similarity with other music. The largest five cosine similarities are used as recommendations.<br />
[[File:Cosine441.png|frame|100px|none|Cosine Similarity]]<br />
<br />
== Evaluation Metrics ==<br />
=== Precision: ===<br />
* The proportion of True Positives with respect to the '''predicted''' positive cases (true positives and false positives)<br />
* For example, out of all the songs that the classifier '''predicted''' as Classical, how many are actually Classical?<br />
* Describes the rate at which the classifier predicts the true genre of songs among those predicted to be of that certain genre<br />
<br />
=== Recall: ===<br />
* The proportion of True Positives with respect to the '''actual''' positive cases (true positives and false negatives)<br />
* For example, out of all the songs that are '''actually''' Classical, how many are correctly predicted to be Classical?<br />
* Describes the rate at which the classifier predicts the true genre of songs among the correct instances of that genre<br />
<br />
=== F1-Score: ===<br />
An accuracy metric that combines the classifier’s precision and recall scores by taking the harmonic mean between the two metrics:<br />
<br />
[[File:F1441.png|frame|100px|none|F1-Score]]<br />
<br />
=== Receiver operating characteristics (ROC): ===<br />
* A graphical metric that is used to assess a classification model at different classification thresholds <br />
* In the case of a classification threshold of 0.5, this means that if <math>P(Y = k | X = x) > 0.5</math> then we classify this instance as class k<br />
* Plots the true positive rate versus false positive rate as the classification threshold is varied<br />
<br />
[[File:ROCGraph.jpg|thumb|400px|none|ROC Graph. Comparison of True Positive Rate and False Positive Rate]]<br />
<br />
=== Area Under the Curve (AUC) ===<br />
AUC is the area under the ROC in doing so, the ROC provides an aggregate measure across all possible classification thresholds.<br />
<br />
In the context of the paper: When scoring all songs as <math>Prob(Classical | X=x)</math>, it is the probability that the model ranks a random Classical song at a higher probability than a random non-Classical song.<br />
<br />
[[File:AUCGraph.jpg|thumb|400px|none|Area under the ROC curve.]]<br />
<br />
== Results ==<br />
=== Accuracy Metrics ===<br />
The table below is the accuracy metrics with the classification threshold of 0.5.<br />
<br />
[[File:TruePositiveChart.jpg|thumb|none|True Positive / False Positive Chart]]<br />
On average, CRNN outperforms CNN in true positive and false positive cases. In addition, it is very apparent that false positives are much more frequent for songs in the Instrumental genre, perhaps indicating that more pre-processing needs to be done for songs in this genre or that it should be excluded from analysis completely given how most music has instrumental components.<br />
<br />
<br />
[[File:F1Chart441.jpg|thumb|400px|none|F1 Chart]]<br />
On average, CRNN outperforms CNN in F1-score. <br />
<br />
<br />
[[File:AUCChart.jpg|thumb|400px|none|AUC Chart]]<br />
On average, CRNN also outperforms CNN in AUC metric.<br />
<br />
<br />
CRNN models that consider the frequency features and time sequence patterns of songs have a better classification performance through metrics such as F1 score and AUC when comparing to CNN classifier.<br />
<br />
=== Evaluation of Music Recommendation System: ===<br />
<br />
* A listening experiment was performed with 30 participants to access user responses to given music recommendations.<br />
* Participants choose 5 pieces of music they enjoyed and the recommender system generated 5 new recommendations. The participants then evaluated the music recommendation by recording whether the song was liked or disliked.<br />
* The recommendation system takes two approaches to the recommendation:<br />
** Method one uses only the value of cosine similarity.<br />
** Method two uses the value of cosine similarity and information on music genre.<br />
*Perform test of significance of differences in average user likes between the two methods using a t-statistic:<br />
[[File:H0441.png|frame|100px|none|Hypothesis test between method 1 and method 2]]<br />
<br />
Comparing the two methods, <math> H_0: u_1 - u_2 = 0</math>, we have <math> t_{stat} = -4.743 < -2.037 </math>, which demonstrates that the increase in average user likes with the addition of music genre information is statistically significant.<br />
<br />
== Conclusion: ==<br />
<br />
The two two main conclusions obtained from this paper:<br />
<br />
* The music genre should be a key feature to increase the predictive capabilities of the music recommendation system.<br />
<br />
* To extract the song genre from a song’s audio signals and get overall better performance, CRNN’s are superior to CNN’s as they consider frequency in features and time sequence patterns of audio signals. <br />
<br />
According to the paper, the authors suggested adding other music features like tempo gram for capturing local tempo as a way to improve the accuracy of the recommender system.<br />
<br />
== Critiques/ Insights: ==<br />
# It would be helpful if authors bench-mark their novel approach with other recommendation algorithms such as collaborative filtering to see if there is a lift in predictive capabilities.<br />
# The listening experiment used to evaluate the recommendation system only includes songs that are outputted by the model. Users may be biased if they believe all songs have come from a recommendation system. To remove bias, we suggest having 15 songs where 5 songs are recommended and 10 songs are set. With this in the user’s mind, it may remove some bias in response and give more accurate predictive capabilities. <br />
# It would be better if they go into more details about how CRNN makes it perform better than CNN, in terms of attributes of each network.<br />
# The methodology introduced in this paper is probably also suitable for movie recommendations. As music is presented as spectrograms (images) in a time sequence, and it is very similar to a movie. <br />
# The way of evaluation is a very interesting approach. Since it's usually not easy to evaluate the testing result when it's subjective. By listing all these evaluations' performance, the result would be more comprehensive. A practice that might reduce bias is by coming back to the participants after a couple of days and asking whether they liked the music that was recommended. Often times music "grows" on people and their opinion of a new song may change after some time has passed. <br />
# The paper lacks the comparison between the proposed algorithm and the music recommendation algorithms being used now. It will be clearer to show the superiority of this algorithm.<br />
# The GAN neural network has been proposed to enhance the performance of the neural network, so an improved result may appear after considering using GAN.<br />
# The limitation of CNN and CRNN could be that they are only able to process the spectrograms with single labels rather than multiple labels. This is far from enough for the music recommender systems in today's music industry since the edges between various genres are blurred.<br />
# Is it possible for CNN and CRNN to identify different songs? The model would be harder to train, based on my experience, the efficiency of CNN in R is not very high, which can be improved for future work.<br />
# According to the author, the recommender system is done by calculating the cosine similarity of extraction features from one music to another music. Is possible to represent it by Euclidean distance or p-norm distances?<br />
# In real-life application, most of the music software will have the ability to recommend music to the listener and ask do they like the music that was recommended. It would be a nice application by involving some new information from the listener.<br />
# Actual music listeners do not listen to one genre of music, and in fact listening to the same track or the same genre would be somewhat unusual. Could this method be used to make recommendations not on genre, but based on other categories? (Such as the theme of the lyrics, the pitch of the singer, or the date published). Would this model be able to differentiate between tracks of varying "lyric vocabulation difficulty"? Or would NLP algorithms be needed to consider lyrics?<br />
# This model can be applied to many other fields such as recommending the news in the news app, recommending things to buy in the amazon, recommending videos to watch in YOUTUBE and so on based on the user information.<br />
# Looks like for the most genres, CRNN outperforms CNN, but CNN did do better on a few genres (like Jazz), so it might be better to mix them together or might use CNN for some genres and CRNN for the rest.<br />
# Cosine similarity is used to find songs with similar patterns as the input ones from users. That is, feature variables are extracted from the trained neural network model before the classification layer, and used as the basis to find similar songs. One potential problem of this approach is that if the neural network classifies an input song incorrectly, the extracted feature vector will not be a good representation of the input song. Thus, a song that is in fact really similar to the input song may have a small cosine similarity value, i.e. not be recommended. In conclusion, if the first classification is wrong, future inferences based on that is going to make it deviate further from the true answer. A possible future improvement will be how to offset this inference error.<br />
# In the tables when comparing performance and accuracies of the CNN and CRNN models on different genres of music, the researchers claimed that CRNN had superior performance to CNN models. This seemed intuitive, especially in the cases when the differences in accuracies were large. However, maybe the researchers should consider including some hypothesis testing statistics in such tables, which would support such claims in a more rigorous manner.<br />
# A music recommender system that doesn't use the song's meta data such as artist and genre and rather tries to classify genre itself seems unproductive. I also believe that the specific artist matters much more than the genre since within a genre you have many different styles. It just seems like the authors hamstring their recommender system by excluding other relevant data.<br />
# The genres that are posed in the paper are very broad and may not be specific enough to distinguish a listeners actual tastes (ie, I like rock and roll, but not punk rock, which could both be in the "rock" category). It would be interesting to run similar experiments with more concrete and specific genres to study the possibility of improving accuracy in the model.<br />
# This summary is well organized with detailed explanation to the music recommendation algorithm. However, since the data used in this paper is cleaned to buffer the efficiency of the recommendation, there should be a section evaluating the impact of noise on the performance this algorithm and how to minimize the impact.<br />
# This method will be better if the user choose some certain music genres that they like while doing the sign-up process. This is similar to recommending articles on twitter.<br />
# I have some feedback for the "Evaluation of Music Recommendation System" section. Firstly, there can be a brief mention of the participants' background information. Secondly, the summary mentions that "participants choose 5 pieces of music they enjoyed". Are they free to choose any music they like, or are they choosing from a pool of selections? What are the lengths of these music pieces? Lastly, method one and method two are compared against each other. It's intuitive that method two will outperform method one, since method two makes use of both cosine similarity and information on music genre, whereas method one only makes use of cosine similarity. Thus, saying method two outperforms method one is not necessarily surprising. I would like to see more explanation on why these methods are chosen, and why comparing them directly is considered to be fair.<br />
# It would be better to have more comparison with other existing music recommender system.<br />
# In the Collecting Music Data section, the author has indicated that for maintaining the balance of data for each genre that they are choosing to omit some genres and a portion of the dataset. However, how this was done was not explained explicitly which can be a concern for results replication. It would be better to describe the steps and measures taken to ensure the actions taken by the teams are reproducible. <br />
# For cleaning data, for training purposes, the team is choosing to omit the ones with lower music quality. While this is a sound option, it can be adjusted that the ratings for the music are deducted to adjust the balance. This could be important since a poor music quality could mean either equipment failure or corrupt server storage or it was a recording of a live performance that often does not have a perfect studio quality yet it would be loved by many real-life users. This omission is not entirely justified and feels like a deliberate adjustment for later results.<br />
# It would be more convincing if the author could provide more comparison between CRNN and CNN.<br />
# How is the result used to recommend songs within genres? It looks like it only predicts what genre the user likes to listen and recommends one of the songs from that genre. How can this recommender system be used to recommend songs within the same genre?<br />
# This [https://arxiv.org/pdf/2006.15795.pdf paper] implements CRNN differently; the CNN and RNN are separate and their resulting matrices and combined later. Would using this version of the CRNN potentially improve the accuracy?<br />
# This kind of approach can be used in implementing other recommender systems for, like movies, articles, news, websites etc. It would be helpful if the author could explain and generalize the implementation on other forms of recommender systems.<br />
# The accuracy of the genre classifier seemed really low, considering how distinct the genres sound to humans. The authors recommend adding features to the data but these could likely be extracted from the audio signal. Extra preprocessing would likely go a long way to improve the accuracy.<br />
# Since it was mentioned that different genres were used, it would be interesting to know if the model can classify different languages and how it performs with songs in different languages.<br />
# It is possible to extend this application to classifying baroque, classical, and romantic genre music. This can be beneficial for students (and frankly, people of all ages) who are learning about music. What's even more interesting to see is if this algorithm can distinguish music pieces written by classical musicians such as Beethoven, Haydn, and Mozart. Of course, it would take more effort in distinguishing features across the music pieces of these three artists, but it's an area worth exploring.<br />
<br />
== References: ==<br />
Nilashi, M., et.al. ''Collaborative Filtering Recommender Systems''. Research Journal of Applied Sciences, Engineering and Technology 5(16):4168-4182, 2013.<br />
Adiyansjah, Alexander A S Gunawan, Derwin Suhartono, Music Recommender System Based on Genre using Convolutional Recurrent Neural Networks, Procedia Computer Science, https://doi.org/10.1016/j.procs.2019.08.146.</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Music_Recommender_System_Based_using_CRNN&diff=49407Music Recommender System Based using CRNN2020-12-06T16:40:39Z<p>Jcllau: /* Critiques/ Insights: */</p>
<hr />
<div>==Introduction and Objective:==<br />
<br />
In the digital era of music streaming, companies, such as Spotify and Pandora, are faced with the following challenge: can they provide users with relevant and personalized music recommendations amidst the ever-growing abundance of music and user data?<br />
<br />
The objective of this paper is to implement a personalized music recommender system that takes user listening history as input and continually finds new music that captures individual user preferences.<br />
<br />
This paper argues that a music recommendation system should vary from the general recommendation system used in practice since it should combine music feature recognition and audio processing technologies to extract music features, and combine them with data on user preferences.<br />
<br />
The authors of this paper took a content-based music approach to build the recommendation system - specifically, comparing the similarity of features based on the audio signal.<br />
<br />
The following two-method approach for building the recommendation system was followed:<br />
#Make recommendations including genre information extracted from classification algorithms.<br />
#Make recommendations without genre information.<br />
<br />
The authors used convolutional recurrent neural networks (CRNN), which is a combination of convolutional neural networks (CNN) and recurrent neural network(RNN), as their main classification model.<br />
<br />
==Methods and Techniques:==<br />
Generally, a music recommender can be divided into three main parts: (i) users, (ii) items, and (iii) user-item matching algorithms. Firstly, a model for a user's music taste is generated based on their profiles. Secondly, item profiling based on editorial, cultural, and acoustic metadata is exploited to increase listener satisfaction. Thirdly, a matching algorithm is employed to recommend personalized music to the listener. Two main approaches are currently available;<br />
<br />
1. Collaborative filtering<br />
<br />
It is based on users' historical listening data and depends on user ratings. Nearest neighbour is the standard method used for collaborative filtering and can be broken into two classes of methods: (i) user-based neighbourhood methods and (ii) item-based neighbourhood methods. <br />
<br />
User-based neighbourhood methods calculate the similarity between the target user and other users, and selects the k most similar. A weighted average of the most similar users' song ratings is then computed to predict how the target user would rate those songs. Songs that have a high predicted rating are then recommended to the user. In contrast, methods that use item-based neighbourhoods calculate similarities between songs that the target user has rated well and songs they have not listened to in order to recommend songs.<br />
<br />
That being said, collaborative filtering faces many challenges. For example, given that each user sees only a small portion of all music libraries, sparsity and scalability become an issue. However, this can be dealt with using matrix factorization. A more difficult challenge to overcome is the fact that users often don't rate songs when they are listening to music. <br />
<br />
2. Content-based filtering<br />
<br />
Content based recommendation systems base their recommendations on the similarity of an items features and features that the user has enjoyed. It has two-steps; (i) Extract audio content features and (ii) predict user preferences.<br />
<br />
In this work, the authors take a content-based approach, as they compare the similarity of audio signal features to make recommendations. To classify music, the original music’s audio signal is converted into a spectrogram image. Using the image and the Short Time Fourier Transform (STFT), we convert the data into the Mel scale which is used in the CNN and CRNN models. <br />
=== Mel Scale: === <br />
The scale of pitches that are heard by listeners, which translates to equal pitch increments.<br />
<br />
[[File:Mel.png|frame|none|Mel Scale on Spectrogram]]<br />
<br />
=== Short Time Fourier Transform (STFT): ===<br />
The transformation that determines the sinusoidal frequency of the audio, with a Hanning smoothing function. In the continuous case this is written as: <math>\mathbf{STFT}\{x(t)\}(\tau,\omega) \equiv X(\tau, \omega) = \int_{-\infty}^{\infty} x(t) w(t-\tau) e^{-i \omega t} \, d t </math><br />
<br />
where: <math>w(\tau)</math> is the Hanning smoothing function. The STFT is applied over a specified window length at a certain time allowing the frequency to represented for that given window rather than the entire signal as a typical Fourier Transform would.<br />
<br />
=== Convolutional Neural Network (CNN): ===<br />
A Convolutional Neural Network is a Neural Network that uses convolution in place of matrix multiplication for some layer calculations. By training the data, weights for inputs are updated to find the most significant data relevant to classification. These convolutional layers gather small groups of data with kernels and try to find patterns that can help find features in the overall data. The features are then used for classification. Padding is another technique used to extend the pixels on the edge of the original image to allow the kernel to more accurately capture the borderline pixels. Padding is also used if one wishes the convolved output image to have a certain size. The image on the left represents the mathematical expression of a convolution operation, while the right image demonstrates an application of a kernel on the data.<br />
<br />
[[File:Convolution.png|thumb|400px|left|Convolution Operation]]<br />
[[File:PaddingKernels.png|thumb|400px|center|Example of Padding (white 0s) and Kernels (blue square)]]<br />
<br />
=== Convolutional Recurrent Neural Network (CRNN): === <br />
The CRNN is similar to the architecture of a CNN, but with the addition of a GRU, which is a Recurrent Neural Network (RNN). An RNN is used to treat sequential data, by reusing the activation function of previous nodes to update the output. A Gated Recurrent Unit (GRU) is used to store more long-term memory and will help train the early hidden layers. GRUs can be thought of as LSTMs but with a forget gate, and has fewer parameters than an LSTM. These gates are used to determine how much information from the past should be passed along onto the future. They are originally aimed to prevent the vanishing gradient problem, since deeper networks will result in smaller and smaller gradients at each layer. The GRU can choose to copy over all the information in the past, thus eliminating the risk of vanishing gradients.<br />
<br />
[[File:GRU441.png|thumb|400px|left|Gated Recurrent Unit (GRU)]]<br />
[[File:Recurrent441.png|thumb|400px|center|Diagram of General Recurrent Neural Network]]<br />
<br />
==Data Screening:==<br />
<br />
The authors of this paper used a publicly available music dataset made up of 25,000 30-second songs from the Free Music Archives which contains 16 different genres. The data is cleaned up by removing low audio quality songs, wrongly labelled genres and those that have multiple genres. To ensure a balanced dataset, only 1000 songs each from the genres of classical, electronic, folk, hip-hop, instrumental, jazz and rock were used in the final model. <br />
<br />
[[File:Data441.png|thumb|200px|none|Data sorted by music genre]]<br />
<br />
==Implementation:==<br />
<br />
=== Modeling Neural Networks ===<br />
<br />
As noted previously, both CNNs and CRNNs were used to model the data. The advantage of CRNNs is that they are able to model time sequence patterns in addition to frequency features from the spectrogram, allowing for greater identification of important features. Furthermore, feature vectors produced before the classification stage could be used to improve accuracy. <br />
<br />
In implementing the neural networks, the Mel-spectrogram data was split up into training, validation, and test sets at a ratio of 8:1:1 respectively and labelled via one-hot encoding. This made it possible for the categorical data to be labelled correctly for binary classification. As opposed to classical stochastic gradient descent, the authors opted to use binary classier and ADAM optimization to update weights in the training phase, and parameters of <math>\alpha = 0.001, \beta_1 = 0.9, \beta_2 = 0.999</math>. Binary cross-entropy was used as the loss function. <br />
Input spectrogram image are 96x1366. In both the CNN and CRNN models, the data was trained over 100 epochs and batch size of 50 (limited computing power) with a binary cross-entropy loss function. Notable model specific details are below:<br />
<br />
'''CNN'''<br />
* Five convolutional layers with 3x3 kernel, stride 1, padding, batch normalization, and ReLU activation<br />
* Max pooling layers <br />
* The sigmoid function was used as the output layer<br />
<br />
'''CRNN'''<br />
* Four convolutional layers with 3x3 kernel (which construct a 2D temporal pattern - two layers of RNNs with Gated Recurrent Units), stride 1, padding, batch normalization, ReLU activation, and dropout rate 0.1<br />
* Feature maps are N x1x15 (N = number of features maps, 68 feature maps in this case) is used for RNNs.<br />
* 4 Max pooling layers for four convolutional layers with kernel ((2x2)-(3x3)-(4x4)-(4x4)) and same stride<br />
* The sigmoid function was used as the output layer<br />
<br />
The CNN and CRNN architecture is also given in the charts below.<br />
<br />
[[File:CNN441.png|thumb|800px|none|Implementation of CNN Model]]<br />
[[File:CRNN441.png|thumb|800px|none|Implementation of CRNN Model]]<br />
<br />
=== Music Recommendation System ===<br />
<br />
The recommendation system is computed by the cosine similarity of the extraction features from the neural network. Each genre will have a song act as a centre point for each class. The final inputs of the trained neural networks will be the feature variables. The featured variables will be used in the cosine similarity to find the best recommendations. <br />
<br />
The values are between [-1,1], where larger values are songs that have similar features. When the user inputs five songs, those songs become the new inputs in the neural networks and the features are used by the cosine similarity with other music. The largest five cosine similarities are used as recommendations.<br />
[[File:Cosine441.png|frame|100px|none|Cosine Similarity]]<br />
<br />
== Evaluation Metrics ==<br />
=== Precision: ===<br />
* The proportion of True Positives with respect to the '''predicted''' positive cases (true positives and false positives)<br />
* For example, out of all the songs that the classifier '''predicted''' as Classical, how many are actually Classical?<br />
* Describes the rate at which the classifier predicts the true genre of songs among those predicted to be of that certain genre<br />
<br />
=== Recall: ===<br />
* The proportion of True Positives with respect to the '''actual''' positive cases (true positives and false negatives)<br />
* For example, out of all the songs that are '''actually''' Classical, how many are correctly predicted to be Classical?<br />
* Describes the rate at which the classifier predicts the true genre of songs among the correct instances of that genre<br />
<br />
=== F1-Score: ===<br />
An accuracy metric that combines the classifier’s precision and recall scores by taking the harmonic mean between the two metrics:<br />
<br />
[[File:F1441.png|frame|100px|none|F1-Score]]<br />
<br />
=== Receiver operating characteristics (ROC): ===<br />
* A graphical metric that is used to assess a classification model at different classification thresholds <br />
* In the case of a classification threshold of 0.5, this means that if <math>P(Y = k | X = x) > 0.5</math> then we classify this instance as class k<br />
* Plots the true positive rate versus false positive rate as the classification threshold is varied<br />
<br />
[[File:ROCGraph.jpg|thumb|400px|none|ROC Graph. Comparison of True Positive Rate and False Positive Rate]]<br />
<br />
=== Area Under the Curve (AUC) ===<br />
AUC is the area under the ROC in doing so, the ROC provides an aggregate measure across all possible classification thresholds.<br />
<br />
In the context of the paper: When scoring all songs as <math>Prob(Classical | X=x)</math>, it is the probability that the model ranks a random Classical song at a higher probability than a random non-Classical song.<br />
<br />
[[File:AUCGraph.jpg|thumb|400px|none|Area under the ROC curve.]]<br />
<br />
== Results ==<br />
=== Accuracy Metrics ===<br />
The table below is the accuracy metrics with the classification threshold of 0.5.<br />
<br />
[[File:TruePositiveChart.jpg|thumb|none|True Positive / False Positive Chart]]<br />
On average, CRNN outperforms CNN in true positive and false positive cases. In addition, it is very apparent that false positives are much more frequent for songs in the Instrumental genre, perhaps indicating that more pre-processing needs to be done for songs in this genre or that it should be excluded from analysis completely given how most music has instrumental components.<br />
<br />
<br />
[[File:F1Chart441.jpg|thumb|400px|none|F1 Chart]]<br />
On average, CRNN outperforms CNN in F1-score. <br />
<br />
<br />
[[File:AUCChart.jpg|thumb|400px|none|AUC Chart]]<br />
On average, CRNN also outperforms CNN in AUC metric.<br />
<br />
<br />
CRNN models that consider the frequency features and time sequence patterns of songs have a better classification performance through metrics such as F1 score and AUC when comparing to CNN classifier.<br />
<br />
=== Evaluation of Music Recommendation System: ===<br />
<br />
* A listening experiment was performed with 30 participants to access user responses to given music recommendations.<br />
* Participants choose 5 pieces of music they enjoyed and the recommender system generated 5 new recommendations. The participants then evaluated the music recommendation by recording whether the song was liked or disliked.<br />
* The recommendation system takes two approaches to the recommendation:<br />
** Method one uses only the value of cosine similarity.<br />
** Method two uses the value of cosine similarity and information on music genre.<br />
*Perform test of significance of differences in average user likes between the two methods using a t-statistic:<br />
[[File:H0441.png|frame|100px|none|Hypothesis test between method 1 and method 2]]<br />
<br />
Comparing the two methods, <math> H_0: u_1 - u_2 = 0</math>, we have <math> t_{stat} = -4.743 < -2.037 </math>, which demonstrates that the increase in average user likes with the addition of music genre information is statistically significant.<br />
<br />
== Conclusion: ==<br />
<br />
The two two main conclusions obtained from this paper:<br />
<br />
* The music genre should be a key feature to increase the predictive capabilities of the music recommendation system.<br />
<br />
* To extract the song genre from a song’s audio signals and get overall better performance, CRNN’s are superior to CNN’s as they consider frequency in features and time sequence patterns of audio signals. <br />
<br />
According to the paper, the authors suggested adding other music features like tempo gram for capturing local tempo as a way to improve the accuracy of the recommender system.<br />
<br />
== Critiques/ Insights: ==<br />
# It would be helpful if authors bench-mark their novel approach with other recommendation algorithms such as collaborative filtering to see if there is a lift in predictive capabilities.<br />
# The listening experiment used to evaluate the recommendation system only includes songs that are outputted by the model. Users may be biased if they believe all songs have come from a recommendation system. To remove bias, we suggest having 15 songs where 5 songs are recommended and 10 songs are set. With this in the user’s mind, it may remove some bias in response and give more accurate predictive capabilities. <br />
# It would be better if they go into more details about how CRNN makes it perform better than CNN, in terms of attributes of each network.<br />
# The methodology introduced in this paper is probably also suitable for movie recommendations. As music is presented as spectrograms (images) in a time sequence, and it is very similar to a movie. <br />
# The way of evaluation is a very interesting approach. Since it's usually not easy to evaluate the testing result when it's subjective. By listing all these evaluations' performance, the result would be more comprehensive. A practice that might reduce bias is by coming back to the participants after a couple of days and asking whether they liked the music that was recommended. Often times music "grows" on people and their opinion of a new song may change after some time has passed. <br />
# The paper lacks the comparison between the proposed algorithm and the music recommendation algorithms being used now. It will be clearer to show the superiority of this algorithm.<br />
# The GAN neural network has been proposed to enhance the performance of the neural network, so an improved result may appear after considering using GAN.<br />
# The limitation of CNN and CRNN could be that they are only able to process the spectrograms with single labels rather than multiple labels. This is far from enough for the music recommender systems in today's music industry since the edges between various genres are blurred.<br />
# Is it possible for CNN and CRNN to identify different songs? The model would be harder to train, based on my experience, the efficiency of CNN in R is not very high, which can be improved for future work.<br />
# According to the author, the recommender system is done by calculating the cosine similarity of extraction features from one music to another music. Is possible to represent it by Euclidean distance or p-norm distances?<br />
# In real-life application, most of the music software will have the ability to recommend music to the listener and ask do they like the music that was recommended. It would be a nice application by involving some new information from the listener.<br />
# Actual music listeners do not listen to one genre of music, and in fact listening to the same track or the same genre would be somewhat unusual. Could this method be used to make recommendations not on genre, but based on other categories? (Such as the theme of the lyrics, the pitch of the singer, or the date published). Would this model be able to differentiate between tracks of varying "lyric vocabulation difficulty"? Or would NLP algorithms be needed to consider lyrics?<br />
# This model can be applied to many other fields such as recommending the news in the news app, recommending things to buy in the amazon, recommending videos to watch in YOUTUBE and so on based on the user information.<br />
# Looks like for the most genres, CRNN outperforms CNN, but CNN did do better on a few genres (like Jazz), so it might be better to mix them together or might use CNN for some genres and CRNN for the rest.<br />
# Cosine similarity is used to find songs with similar patterns as the input ones from users. That is, feature variables are extracted from the trained neural network model before the classification layer, and used as the basis to find similar songs. One potential problem of this approach is that if the neural network classifies an input song incorrectly, the extracted feature vector will not be a good representation of the input song. Thus, a song that is in fact really similar to the input song may have a small cosine similarity value, i.e. not be recommended. In conclusion, if the first classification is wrong, future inferences based on that is going to make it deviate further from the true answer. A possible future improvement will be how to offset this inference error.<br />
# In the tables when comparing performance and accuracies of the CNN and CRNN models on different genres of music, the researchers claimed that CRNN had superior performance to CNN models. This seemed intuitive, especially in the cases when the differences in accuracies were large. However, maybe the researchers should consider including some hypothesis testing statistics in such tables, which would support such claims in a more rigorous manner.<br />
# A music recommender system that doesn't use the song's meta data such as artist and genre and rather tries to classify genre itself seems unproductive. I also believe that the specific artist matters much more than the genre since within a genre you have many different styles. It just seems like the authors hamstring their recommender system by excluding other relevant data.<br />
# The genres that are posed in the paper are very broad and may not be specific enough to distinguish a listeners actual tastes (ie, I like rock and roll, but not punk rock, which could both be in the "rock" category). It would be interesting to run similar experiments with more concrete and specific genres to study the possibility of improving accuracy in the model.<br />
# This summary is well organized with detailed explanation to the music recommendation algorithm. However, since the data used in this paper is cleaned to buffer the efficiency of the recommendation, there should be a section evaluating the impact of noise on the performance this algorithm and how to minimize the impact.<br />
# This method will be better if the user choose some certain music genres that they like while doing the sign-up process. This is similar to recommending articles on twitter.<br />
# I have some feedback for the "Evaluation of Music Recommendation System" section. Firstly, there can be a brief mention of the participants' background information. Secondly, the summary mentions that "participants choose 5 pieces of music they enjoyed". Are they free to choose any music they like, or are they choosing from a pool of selections? What are the lengths of these music pieces? Lastly, method one and method two are compared against each other. It's intuitive that method two will outperform method one, since method two makes use of both cosine similarity and information on music genre, whereas method one only makes use of cosine similarity. Thus, saying method two outperforms method one is not necessarily surprising. I would like to see more explanation on why these methods are chosen, and why comparing them directly is considered to be fair.<br />
# It would be better to have more comparison with other existing music recommender system.<br />
# In the Collecting Music Data section, the author has indicated that for maintaining the balance of data for each genre that they are choosing to omit some genres and a portion of the dataset. However, how this was done was not explained explicitly which can be a concern for results replication. It would be better to describe the steps and measures taken to ensure the actions taken by the teams are reproducible. <br />
# For cleaning data, for training purposes, the team is choosing to omit the ones with lower music quality. While this is a sound option, it can be adjusted that the ratings for the music are deducted to adjust the balance. This could be important since a poor music quality could mean either equipment failure or corrupt server storage or it was a recording of a live performance that often does not have a perfect studio quality yet it would be loved by many real-life users. This omission is not entirely justified and feels like a deliberate adjustment for later results.<br />
# It would be more convincing if the author could provide more comparison between CRNN and CNN.<br />
# How is the result used to recommend songs within genres? It looks like it only predicts what genre the user likes to listen and recommends one of the songs from that genre. How can this recommender system be used to recommend songs within the same genre?<br />
# This [https://arxiv.org/pdf/2006.15795.pdf paper] implements CRNN differently; the CNN and RNN are separate and their resulting matrices and combined later. Would using this version of the CRNN potentially improve the accuracy?<br />
# This kind of approach can be used in implementing other recommender systems for, like movies, articles, news, websites etc. It would be helpful if the author could explain and generalize the implementation on other forms of recommender systems.<br />
# The accuracy of the genre classifier seemed really low, considering how distinct the genres sound to humans. The authors recommend adding features to the data but these could likely be extracted from the audio signal. Extra preprocessing would likely go a long way to improve the accuracy.<br />
# Since it was mentioned that different genres were used, it would be interesting to know if the model can classify different languages and how it performs with songs in different languages.<br />
# It is possible to extend this application to classifying baroque, classical, and romantic genre music. This can be beneficial for students (and frankly, people of all ages) who are learning about music. What's even more interesting to see is if this algorithm can distinguish music pieces written by classical musicians such as Beethoven, Haydn, and Mozart. Of course, it would take more effort in distinguishing features across the music pieces of these three artists, but it's an application worth exploring.<br />
<br />
== References: ==<br />
Nilashi, M., et.al. ''Collaborative Filtering Recommender Systems''. Research Journal of Applied Sciences, Engineering and Technology 5(16):4168-4182, 2013.<br />
Adiyansjah, Alexander A S Gunawan, Derwin Suhartono, Music Recommender System Based on Genre using Convolutional Recurrent Neural Networks, Procedia Computer Science, https://doi.org/10.1016/j.procs.2019.08.146.</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Music_Recommender_System_Based_using_CRNN&diff=49406Music Recommender System Based using CRNN2020-12-06T16:40:26Z<p>Jcllau: /* Critiques/ Insights: */</p>
<hr />
<div>==Introduction and Objective:==<br />
<br />
In the digital era of music streaming, companies, such as Spotify and Pandora, are faced with the following challenge: can they provide users with relevant and personalized music recommendations amidst the ever-growing abundance of music and user data?<br />
<br />
The objective of this paper is to implement a personalized music recommender system that takes user listening history as input and continually finds new music that captures individual user preferences.<br />
<br />
This paper argues that a music recommendation system should vary from the general recommendation system used in practice since it should combine music feature recognition and audio processing technologies to extract music features, and combine them with data on user preferences.<br />
<br />
The authors of this paper took a content-based music approach to build the recommendation system - specifically, comparing the similarity of features based on the audio signal.<br />
<br />
The following two-method approach for building the recommendation system was followed:<br />
#Make recommendations including genre information extracted from classification algorithms.<br />
#Make recommendations without genre information.<br />
<br />
The authors used convolutional recurrent neural networks (CRNN), which is a combination of convolutional neural networks (CNN) and recurrent neural network(RNN), as their main classification model.<br />
<br />
==Methods and Techniques:==<br />
Generally, a music recommender can be divided into three main parts: (i) users, (ii) items, and (iii) user-item matching algorithms. Firstly, a model for a user's music taste is generated based on their profiles. Secondly, item profiling based on editorial, cultural, and acoustic metadata is exploited to increase listener satisfaction. Thirdly, a matching algorithm is employed to recommend personalized music to the listener. Two main approaches are currently available;<br />
<br />
1. Collaborative filtering<br />
<br />
It is based on users' historical listening data and depends on user ratings. Nearest neighbour is the standard method used for collaborative filtering and can be broken into two classes of methods: (i) user-based neighbourhood methods and (ii) item-based neighbourhood methods. <br />
<br />
User-based neighbourhood methods calculate the similarity between the target user and other users, and selects the k most similar. A weighted average of the most similar users' song ratings is then computed to predict how the target user would rate those songs. Songs that have a high predicted rating are then recommended to the user. In contrast, methods that use item-based neighbourhoods calculate similarities between songs that the target user has rated well and songs they have not listened to in order to recommend songs.<br />
<br />
That being said, collaborative filtering faces many challenges. For example, given that each user sees only a small portion of all music libraries, sparsity and scalability become an issue. However, this can be dealt with using matrix factorization. A more difficult challenge to overcome is the fact that users often don't rate songs when they are listening to music. <br />
<br />
2. Content-based filtering<br />
<br />
Content based recommendation systems base their recommendations on the similarity of an items features and features that the user has enjoyed. It has two-steps; (i) Extract audio content features and (ii) predict user preferences.<br />
<br />
In this work, the authors take a content-based approach, as they compare the similarity of audio signal features to make recommendations. To classify music, the original music’s audio signal is converted into a spectrogram image. Using the image and the Short Time Fourier Transform (STFT), we convert the data into the Mel scale which is used in the CNN and CRNN models. <br />
=== Mel Scale: === <br />
The scale of pitches that are heard by listeners, which translates to equal pitch increments.<br />
<br />
[[File:Mel.png|frame|none|Mel Scale on Spectrogram]]<br />
<br />
=== Short Time Fourier Transform (STFT): ===<br />
The transformation that determines the sinusoidal frequency of the audio, with a Hanning smoothing function. In the continuous case this is written as: <math>\mathbf{STFT}\{x(t)\}(\tau,\omega) \equiv X(\tau, \omega) = \int_{-\infty}^{\infty} x(t) w(t-\tau) e^{-i \omega t} \, d t </math><br />
<br />
where: <math>w(\tau)</math> is the Hanning smoothing function. The STFT is applied over a specified window length at a certain time allowing the frequency to represented for that given window rather than the entire signal as a typical Fourier Transform would.<br />
<br />
=== Convolutional Neural Network (CNN): ===<br />
A Convolutional Neural Network is a Neural Network that uses convolution in place of matrix multiplication for some layer calculations. By training the data, weights for inputs are updated to find the most significant data relevant to classification. These convolutional layers gather small groups of data with kernels and try to find patterns that can help find features in the overall data. The features are then used for classification. Padding is another technique used to extend the pixels on the edge of the original image to allow the kernel to more accurately capture the borderline pixels. Padding is also used if one wishes the convolved output image to have a certain size. The image on the left represents the mathematical expression of a convolution operation, while the right image demonstrates an application of a kernel on the data.<br />
<br />
[[File:Convolution.png|thumb|400px|left|Convolution Operation]]<br />
[[File:PaddingKernels.png|thumb|400px|center|Example of Padding (white 0s) and Kernels (blue square)]]<br />
<br />
=== Convolutional Recurrent Neural Network (CRNN): === <br />
The CRNN is similar to the architecture of a CNN, but with the addition of a GRU, which is a Recurrent Neural Network (RNN). An RNN is used to treat sequential data, by reusing the activation function of previous nodes to update the output. A Gated Recurrent Unit (GRU) is used to store more long-term memory and will help train the early hidden layers. GRUs can be thought of as LSTMs but with a forget gate, and has fewer parameters than an LSTM. These gates are used to determine how much information from the past should be passed along onto the future. They are originally aimed to prevent the vanishing gradient problem, since deeper networks will result in smaller and smaller gradients at each layer. The GRU can choose to copy over all the information in the past, thus eliminating the risk of vanishing gradients.<br />
<br />
[[File:GRU441.png|thumb|400px|left|Gated Recurrent Unit (GRU)]]<br />
[[File:Recurrent441.png|thumb|400px|center|Diagram of General Recurrent Neural Network]]<br />
<br />
==Data Screening:==<br />
<br />
The authors of this paper used a publicly available music dataset made up of 25,000 30-second songs from the Free Music Archives which contains 16 different genres. The data is cleaned up by removing low audio quality songs, wrongly labelled genres and those that have multiple genres. To ensure a balanced dataset, only 1000 songs each from the genres of classical, electronic, folk, hip-hop, instrumental, jazz and rock were used in the final model. <br />
<br />
[[File:Data441.png|thumb|200px|none|Data sorted by music genre]]<br />
<br />
==Implementation:==<br />
<br />
=== Modeling Neural Networks ===<br />
<br />
As noted previously, both CNNs and CRNNs were used to model the data. The advantage of CRNNs is that they are able to model time sequence patterns in addition to frequency features from the spectrogram, allowing for greater identification of important features. Furthermore, feature vectors produced before the classification stage could be used to improve accuracy. <br />
<br />
In implementing the neural networks, the Mel-spectrogram data was split up into training, validation, and test sets at a ratio of 8:1:1 respectively and labelled via one-hot encoding. This made it possible for the categorical data to be labelled correctly for binary classification. As opposed to classical stochastic gradient descent, the authors opted to use binary classier and ADAM optimization to update weights in the training phase, and parameters of <math>\alpha = 0.001, \beta_1 = 0.9, \beta_2 = 0.999</math>. Binary cross-entropy was used as the loss function. <br />
Input spectrogram image are 96x1366. In both the CNN and CRNN models, the data was trained over 100 epochs and batch size of 50 (limited computing power) with a binary cross-entropy loss function. Notable model specific details are below:<br />
<br />
'''CNN'''<br />
* Five convolutional layers with 3x3 kernel, stride 1, padding, batch normalization, and ReLU activation<br />
* Max pooling layers <br />
* The sigmoid function was used as the output layer<br />
<br />
'''CRNN'''<br />
* Four convolutional layers with 3x3 kernel (which construct a 2D temporal pattern - two layers of RNNs with Gated Recurrent Units), stride 1, padding, batch normalization, ReLU activation, and dropout rate 0.1<br />
* Feature maps are N x1x15 (N = number of features maps, 68 feature maps in this case) is used for RNNs.<br />
* 4 Max pooling layers for four convolutional layers with kernel ((2x2)-(3x3)-(4x4)-(4x4)) and same stride<br />
* The sigmoid function was used as the output layer<br />
<br />
The CNN and CRNN architecture is also given in the charts below.<br />
<br />
[[File:CNN441.png|thumb|800px|none|Implementation of CNN Model]]<br />
[[File:CRNN441.png|thumb|800px|none|Implementation of CRNN Model]]<br />
<br />
=== Music Recommendation System ===<br />
<br />
The recommendation system is computed by the cosine similarity of the extraction features from the neural network. Each genre will have a song act as a centre point for each class. The final inputs of the trained neural networks will be the feature variables. The featured variables will be used in the cosine similarity to find the best recommendations. <br />
<br />
The values are between [-1,1], where larger values are songs that have similar features. When the user inputs five songs, those songs become the new inputs in the neural networks and the features are used by the cosine similarity with other music. The largest five cosine similarities are used as recommendations.<br />
[[File:Cosine441.png|frame|100px|none|Cosine Similarity]]<br />
<br />
== Evaluation Metrics ==<br />
=== Precision: ===<br />
* The proportion of True Positives with respect to the '''predicted''' positive cases (true positives and false positives)<br />
* For example, out of all the songs that the classifier '''predicted''' as Classical, how many are actually Classical?<br />
* Describes the rate at which the classifier predicts the true genre of songs among those predicted to be of that certain genre<br />
<br />
=== Recall: ===<br />
* The proportion of True Positives with respect to the '''actual''' positive cases (true positives and false negatives)<br />
* For example, out of all the songs that are '''actually''' Classical, how many are correctly predicted to be Classical?<br />
* Describes the rate at which the classifier predicts the true genre of songs among the correct instances of that genre<br />
<br />
=== F1-Score: ===<br />
An accuracy metric that combines the classifier’s precision and recall scores by taking the harmonic mean between the two metrics:<br />
<br />
[[File:F1441.png|frame|100px|none|F1-Score]]<br />
<br />
=== Receiver operating characteristics (ROC): ===<br />
* A graphical metric that is used to assess a classification model at different classification thresholds <br />
* In the case of a classification threshold of 0.5, this means that if <math>P(Y = k | X = x) > 0.5</math> then we classify this instance as class k<br />
* Plots the true positive rate versus false positive rate as the classification threshold is varied<br />
<br />
[[File:ROCGraph.jpg|thumb|400px|none|ROC Graph. Comparison of True Positive Rate and False Positive Rate]]<br />
<br />
=== Area Under the Curve (AUC) ===<br />
AUC is the area under the ROC in doing so, the ROC provides an aggregate measure across all possible classification thresholds.<br />
<br />
In the context of the paper: When scoring all songs as <math>Prob(Classical | X=x)</math>, it is the probability that the model ranks a random Classical song at a higher probability than a random non-Classical song.<br />
<br />
[[File:AUCGraph.jpg|thumb|400px|none|Area under the ROC curve.]]<br />
<br />
== Results ==<br />
=== Accuracy Metrics ===<br />
The table below is the accuracy metrics with the classification threshold of 0.5.<br />
<br />
[[File:TruePositiveChart.jpg|thumb|none|True Positive / False Positive Chart]]<br />
On average, CRNN outperforms CNN in true positive and false positive cases. In addition, it is very apparent that false positives are much more frequent for songs in the Instrumental genre, perhaps indicating that more pre-processing needs to be done for songs in this genre or that it should be excluded from analysis completely given how most music has instrumental components.<br />
<br />
<br />
[[File:F1Chart441.jpg|thumb|400px|none|F1 Chart]]<br />
On average, CRNN outperforms CNN in F1-score. <br />
<br />
<br />
[[File:AUCChart.jpg|thumb|400px|none|AUC Chart]]<br />
On average, CRNN also outperforms CNN in AUC metric.<br />
<br />
<br />
CRNN models that consider the frequency features and time sequence patterns of songs have a better classification performance through metrics such as F1 score and AUC when comparing to CNN classifier.<br />
<br />
=== Evaluation of Music Recommendation System: ===<br />
<br />
* A listening experiment was performed with 30 participants to access user responses to given music recommendations.<br />
* Participants choose 5 pieces of music they enjoyed and the recommender system generated 5 new recommendations. The participants then evaluated the music recommendation by recording whether the song was liked or disliked.<br />
* The recommendation system takes two approaches to the recommendation:<br />
** Method one uses only the value of cosine similarity.<br />
** Method two uses the value of cosine similarity and information on music genre.<br />
*Perform test of significance of differences in average user likes between the two methods using a t-statistic:<br />
[[File:H0441.png|frame|100px|none|Hypothesis test between method 1 and method 2]]<br />
<br />
Comparing the two methods, <math> H_0: u_1 - u_2 = 0</math>, we have <math> t_{stat} = -4.743 < -2.037 </math>, which demonstrates that the increase in average user likes with the addition of music genre information is statistically significant.<br />
<br />
== Conclusion: ==<br />
<br />
The two two main conclusions obtained from this paper:<br />
<br />
* The music genre should be a key feature to increase the predictive capabilities of the music recommendation system.<br />
<br />
* To extract the song genre from a song’s audio signals and get overall better performance, CRNN’s are superior to CNN’s as they consider frequency in features and time sequence patterns of audio signals. <br />
<br />
According to the paper, the authors suggested adding other music features like tempo gram for capturing local tempo as a way to improve the accuracy of the recommender system.<br />
<br />
== Critiques/ Insights: ==<br />
# It would be helpful if authors bench-mark their novel approach with other recommendation algorithms such as collaborative filtering to see if there is a lift in predictive capabilities.<br />
# The listening experiment used to evaluate the recommendation system only includes songs that are outputted by the model. Users may be biased if they believe all songs have come from a recommendation system. To remove bias, we suggest having 15 songs where 5 songs are recommended and 10 songs are set. With this in the user’s mind, it may remove some bias in response and give more accurate predictive capabilities. <br />
# It would be better if they go into more details about how CRNN makes it perform better than CNN, in terms of attributes of each network.<br />
# The methodology introduced in this paper is probably also suitable for movie recommendations. As music is presented as spectrograms (images) in a time sequence, and it is very similar to a movie. <br />
# The way of evaluation is a very interesting approach. Since it's usually not easy to evaluate the testing result when it's subjective. By listing all these evaluations' performance, the result would be more comprehensive. A practice that might reduce bias is by coming back to the participants after a couple of days and asking whether they liked the music that was recommended. Often times music "grows" on people and their opinion of a new song may change after some time has passed. <br />
# The paper lacks the comparison between the proposed algorithm and the music recommendation algorithms being used now. It will be clearer to show the superiority of this algorithm.<br />
# The GAN neural network has been proposed to enhance the performance of the neural network, so an improved result may appear after considering using GAN.<br />
# The limitation of CNN and CRNN could be that they are only able to process the spectrograms with single labels rather than multiple labels. This is far from enough for the music recommender systems in today's music industry since the edges between various genres are blurred.<br />
# Is it possible for CNN and CRNN to identify different songs? The model would be harder to train, based on my experience, the efficiency of CNN in R is not very high, which can be improved for future work.<br />
# According to the author, the recommender system is done by calculating the cosine similarity of extraction features from one music to another music. Is possible to represent it by Euclidean distance or p-norm distances?<br />
# In real-life application, most of the music software will have the ability to recommend music to the listener and ask do they like the music that was recommended. It would be a nice application by involving some new information from the listener.<br />
# Actual music listeners do not listen to one genre of music, and in fact listening to the same track or the same genre would be somewhat unusual. Could this method be used to make recommendations not on genre, but based on other categories? (Such as the theme of the lyrics, the pitch of the singer, or the date published). Would this model be able to differentiate between tracks of varying "lyric vocabulation difficulty"? Or would NLP algorithms be needed to consider lyrics?<br />
# This model can be applied to many other fields such as recommending the news in the news app, recommending things to buy in the amazon, recommending videos to watch in YOUTUBE and so on based on the user information.<br />
# Looks like for the most genres, CRNN outperforms CNN, but CNN did do better on a few genres (like Jazz), so it might be better to mix them together or might use CNN for some genres and CRNN for the rest.<br />
# Cosine similarity is used to find songs with similar patterns as the input ones from users. That is, feature variables are extracted from the trained neural network model before the classification layer, and used as the basis to find similar songs. One potential problem of this approach is that if the neural network classifies an input song incorrectly, the extracted feature vector will not be a good representation of the input song. Thus, a song that is in fact really similar to the input song may have a small cosine similarity value, i.e. not be recommended. In conclusion, if the first classification is wrong, future inferences based on that is going to make it deviate further from the true answer. A possible future improvement will be how to offset this inference error.<br />
# In the tables when comparing performance and accuracies of the CNN and CRNN models on different genres of music, the researchers claimed that CRNN had superior performance to CNN models. This seemed intuitive, especially in the cases when the differences in accuracies were large. However, maybe the researchers should consider including some hypothesis testing statistics in such tables, which would support such claims in a more rigorous manner.<br />
# A music recommender system that doesn't use the song's meta data such as artist and genre and rather tries to classify genre itself seems unproductive. I also believe that the specific artist matters much more than the genre since within a genre you have many different styles. It just seems like the authors hamstring their recommender system by excluding other relevant data.<br />
# The genres that are posed in the paper are very broad and may not be specific enough to distinguish a listeners actual tastes (ie, I like rock and roll, but not punk rock, which could both be in the "rock" category). It would be interesting to run similar experiments with more concrete and specific genres to study the possibility of improving accuracy in the model.<br />
# This summary is well organized with detailed explanation to the music recommendation algorithm. However, since the data used in this paper is cleaned to buffer the efficiency of the recommendation, there should be a section evaluating the impact of noise on the performance this algorithm and how to minimize the impact.<br />
# This method will be better if the user choose some certain music genres that they like while doing the sign-up process. This is similar to recommending articles on twitter.<br />
# I have some feedback for the "Evaluation of Music Recommendation System" section. Firstly, there can be a brief mention of the participants' background information. Secondly, the summary mentions that "participants choose 5 pieces of music they enjoyed". Are they free to choose any music they like, or are they choosing from a pool of selections? What are the lengths of these music pieces? Lastly, method one and method two are compared against each other. It's intuitive that method two will outperform method one, since method two makes use of both cosine similarity and information on music genre, whereas method one only makes use of cosine similarity. Thus, saying method two outperforms method one is not necessarily surprising. I would like to see more explanation on why these methods are chosen, and why comparing them directly is considered to be fair.<br />
# It would be better to have more comparison with other existing music recommender system.<br />
# In the Collecting Music Data section, the author has indicated that for maintaining the balance of data for each genre that they are choosing to omit some genres and a portion of the dataset. However, how this was done was not explained explicitly which can be a concern for results replication. It would be better to describe the steps and measures taken to ensure the actions taken by the teams are reproducible. <br />
# For cleaning data, for training purposes, the team is choosing to omit the ones with lower music quality. While this is a sound option, it can be adjusted that the ratings for the music are deducted to adjust the balance. This could be important since a poor music quality could mean either equipment failure or corrupt server storage or it was a recording of a live performance that often does not have a perfect studio quality yet it would be loved by many real-life users. This omission is not entirely justified and feels like a deliberate adjustment for later results.<br />
# It would be more convincing if the author could provide more comparison between CRNN and CNN.<br />
# How is the result used to recommend songs within genres? It looks like it only predicts what genre the user likes to listen and recommends one of the songs from that genre. How can this recommender system be used to recommend songs within the same genre?<br />
# This [https://arxiv.org/pdf/2006.15795.pdf paper] implements CRNN differently; the CNN and RNN are separate and their resulting matrices and combined later. Would using this version of the CRNN potentially improve the accuracy?<br />
# This kind of approach can be used in implementing other recommender systems for, like movies, articles, news, websites etc. It would be helpful if the author could explain and generalize the implementation on other forms of recommender systems.<br />
# The accuracy of the genre classifier seemed really low, considering how distinct the genres sound to humans. The authors recommend adding features to the data but these could likely be extracted from the audio signal. Extra preprocessing would likely go a long way to improve the accuracy.<br />
# Since it was mentioned that different genres were used, it would be interesting to know if the model can classify different languages and how it performs with songs in different languages.<br />
# It is possible to extend this application to classifying baroque, classical, and romantic genre music. This can be beneficial for students (and frankly, people of all ages) who are learning about music. What's even more interesting to see is if this algorithm can distinguish music pieces written by classical musicians such as Beethoven, Haydn, and Mozart. Of course, it would take more effort in distinguishing features across the music pieces of these three artists, but it's an application worth exploring<br />
<br />
== References: ==<br />
Nilashi, M., et.al. ''Collaborative Filtering Recommender Systems''. Research Journal of Applied Sciences, Engineering and Technology 5(16):4168-4182, 2013.<br />
Adiyansjah, Alexander A S Gunawan, Derwin Suhartono, Music Recommender System Based on Genre using Convolutional Recurrent Neural Networks, Procedia Computer Science, https://doi.org/10.1016/j.procs.2019.08.146.</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Music_Recommender_System_Based_using_CRNN&diff=49405Music Recommender System Based using CRNN2020-12-06T16:38:44Z<p>Jcllau: /* Critiques/ Insights: */</p>
<hr />
<div>==Introduction and Objective:==<br />
<br />
In the digital era of music streaming, companies, such as Spotify and Pandora, are faced with the following challenge: can they provide users with relevant and personalized music recommendations amidst the ever-growing abundance of music and user data?<br />
<br />
The objective of this paper is to implement a personalized music recommender system that takes user listening history as input and continually finds new music that captures individual user preferences.<br />
<br />
This paper argues that a music recommendation system should vary from the general recommendation system used in practice since it should combine music feature recognition and audio processing technologies to extract music features, and combine them with data on user preferences.<br />
<br />
The authors of this paper took a content-based music approach to build the recommendation system - specifically, comparing the similarity of features based on the audio signal.<br />
<br />
The following two-method approach for building the recommendation system was followed:<br />
#Make recommendations including genre information extracted from classification algorithms.<br />
#Make recommendations without genre information.<br />
<br />
The authors used convolutional recurrent neural networks (CRNN), which is a combination of convolutional neural networks (CNN) and recurrent neural network(RNN), as their main classification model.<br />
<br />
==Methods and Techniques:==<br />
Generally, a music recommender can be divided into three main parts: (i) users, (ii) items, and (iii) user-item matching algorithms. Firstly, a model for a user's music taste is generated based on their profiles. Secondly, item profiling based on editorial, cultural, and acoustic metadata is exploited to increase listener satisfaction. Thirdly, a matching algorithm is employed to recommend personalized music to the listener. Two main approaches are currently available;<br />
<br />
1. Collaborative filtering<br />
<br />
It is based on users' historical listening data and depends on user ratings. Nearest neighbour is the standard method used for collaborative filtering and can be broken into two classes of methods: (i) user-based neighbourhood methods and (ii) item-based neighbourhood methods. <br />
<br />
User-based neighbourhood methods calculate the similarity between the target user and other users, and selects the k most similar. A weighted average of the most similar users' song ratings is then computed to predict how the target user would rate those songs. Songs that have a high predicted rating are then recommended to the user. In contrast, methods that use item-based neighbourhoods calculate similarities between songs that the target user has rated well and songs they have not listened to in order to recommend songs.<br />
<br />
That being said, collaborative filtering faces many challenges. For example, given that each user sees only a small portion of all music libraries, sparsity and scalability become an issue. However, this can be dealt with using matrix factorization. A more difficult challenge to overcome is the fact that users often don't rate songs when they are listening to music. <br />
<br />
2. Content-based filtering<br />
<br />
Content based recommendation systems base their recommendations on the similarity of an items features and features that the user has enjoyed. It has two-steps; (i) Extract audio content features and (ii) predict user preferences.<br />
<br />
In this work, the authors take a content-based approach, as they compare the similarity of audio signal features to make recommendations. To classify music, the original music’s audio signal is converted into a spectrogram image. Using the image and the Short Time Fourier Transform (STFT), we convert the data into the Mel scale which is used in the CNN and CRNN models. <br />
=== Mel Scale: === <br />
The scale of pitches that are heard by listeners, which translates to equal pitch increments.<br />
<br />
[[File:Mel.png|frame|none|Mel Scale on Spectrogram]]<br />
<br />
=== Short Time Fourier Transform (STFT): ===<br />
The transformation that determines the sinusoidal frequency of the audio, with a Hanning smoothing function. In the continuous case this is written as: <math>\mathbf{STFT}\{x(t)\}(\tau,\omega) \equiv X(\tau, \omega) = \int_{-\infty}^{\infty} x(t) w(t-\tau) e^{-i \omega t} \, d t </math><br />
<br />
where: <math>w(\tau)</math> is the Hanning smoothing function. The STFT is applied over a specified window length at a certain time allowing the frequency to represented for that given window rather than the entire signal as a typical Fourier Transform would.<br />
<br />
=== Convolutional Neural Network (CNN): ===<br />
A Convolutional Neural Network is a Neural Network that uses convolution in place of matrix multiplication for some layer calculations. By training the data, weights for inputs are updated to find the most significant data relevant to classification. These convolutional layers gather small groups of data with kernels and try to find patterns that can help find features in the overall data. The features are then used for classification. Padding is another technique used to extend the pixels on the edge of the original image to allow the kernel to more accurately capture the borderline pixels. Padding is also used if one wishes the convolved output image to have a certain size. The image on the left represents the mathematical expression of a convolution operation, while the right image demonstrates an application of a kernel on the data.<br />
<br />
[[File:Convolution.png|thumb|400px|left|Convolution Operation]]<br />
[[File:PaddingKernels.png|thumb|400px|center|Example of Padding (white 0s) and Kernels (blue square)]]<br />
<br />
=== Convolutional Recurrent Neural Network (CRNN): === <br />
The CRNN is similar to the architecture of a CNN, but with the addition of a GRU, which is a Recurrent Neural Network (RNN). An RNN is used to treat sequential data, by reusing the activation function of previous nodes to update the output. A Gated Recurrent Unit (GRU) is used to store more long-term memory and will help train the early hidden layers. GRUs can be thought of as LSTMs but with a forget gate, and has fewer parameters than an LSTM. These gates are used to determine how much information from the past should be passed along onto the future. They are originally aimed to prevent the vanishing gradient problem, since deeper networks will result in smaller and smaller gradients at each layer. The GRU can choose to copy over all the information in the past, thus eliminating the risk of vanishing gradients.<br />
<br />
[[File:GRU441.png|thumb|400px|left|Gated Recurrent Unit (GRU)]]<br />
[[File:Recurrent441.png|thumb|400px|center|Diagram of General Recurrent Neural Network]]<br />
<br />
==Data Screening:==<br />
<br />
The authors of this paper used a publicly available music dataset made up of 25,000 30-second songs from the Free Music Archives which contains 16 different genres. The data is cleaned up by removing low audio quality songs, wrongly labelled genres and those that have multiple genres. To ensure a balanced dataset, only 1000 songs each from the genres of classical, electronic, folk, hip-hop, instrumental, jazz and rock were used in the final model. <br />
<br />
[[File:Data441.png|thumb|200px|none|Data sorted by music genre]]<br />
<br />
==Implementation:==<br />
<br />
=== Modeling Neural Networks ===<br />
<br />
As noted previously, both CNNs and CRNNs were used to model the data. The advantage of CRNNs is that they are able to model time sequence patterns in addition to frequency features from the spectrogram, allowing for greater identification of important features. Furthermore, feature vectors produced before the classification stage could be used to improve accuracy. <br />
<br />
In implementing the neural networks, the Mel-spectrogram data was split up into training, validation, and test sets at a ratio of 8:1:1 respectively and labelled via one-hot encoding. This made it possible for the categorical data to be labelled correctly for binary classification. As opposed to classical stochastic gradient descent, the authors opted to use binary classier and ADAM optimization to update weights in the training phase, and parameters of <math>\alpha = 0.001, \beta_1 = 0.9, \beta_2 = 0.999</math>. Binary cross-entropy was used as the loss function. <br />
Input spectrogram image are 96x1366. In both the CNN and CRNN models, the data was trained over 100 epochs and batch size of 50 (limited computing power) with a binary cross-entropy loss function. Notable model specific details are below:<br />
<br />
'''CNN'''<br />
* Five convolutional layers with 3x3 kernel, stride 1, padding, batch normalization, and ReLU activation<br />
* Max pooling layers <br />
* The sigmoid function was used as the output layer<br />
<br />
'''CRNN'''<br />
* Four convolutional layers with 3x3 kernel (which construct a 2D temporal pattern - two layers of RNNs with Gated Recurrent Units), stride 1, padding, batch normalization, ReLU activation, and dropout rate 0.1<br />
* Feature maps are N x1x15 (N = number of features maps, 68 feature maps in this case) is used for RNNs.<br />
* 4 Max pooling layers for four convolutional layers with kernel ((2x2)-(3x3)-(4x4)-(4x4)) and same stride<br />
* The sigmoid function was used as the output layer<br />
<br />
The CNN and CRNN architecture is also given in the charts below.<br />
<br />
[[File:CNN441.png|thumb|800px|none|Implementation of CNN Model]]<br />
[[File:CRNN441.png|thumb|800px|none|Implementation of CRNN Model]]<br />
<br />
=== Music Recommendation System ===<br />
<br />
The recommendation system is computed by the cosine similarity of the extraction features from the neural network. Each genre will have a song act as a centre point for each class. The final inputs of the trained neural networks will be the feature variables. The featured variables will be used in the cosine similarity to find the best recommendations. <br />
<br />
The values are between [-1,1], where larger values are songs that have similar features. When the user inputs five songs, those songs become the new inputs in the neural networks and the features are used by the cosine similarity with other music. The largest five cosine similarities are used as recommendations.<br />
[[File:Cosine441.png|frame|100px|none|Cosine Similarity]]<br />
<br />
== Evaluation Metrics ==<br />
=== Precision: ===<br />
* The proportion of True Positives with respect to the '''predicted''' positive cases (true positives and false positives)<br />
* For example, out of all the songs that the classifier '''predicted''' as Classical, how many are actually Classical?<br />
* Describes the rate at which the classifier predicts the true genre of songs among those predicted to be of that certain genre<br />
<br />
=== Recall: ===<br />
* The proportion of True Positives with respect to the '''actual''' positive cases (true positives and false negatives)<br />
* For example, out of all the songs that are '''actually''' Classical, how many are correctly predicted to be Classical?<br />
* Describes the rate at which the classifier predicts the true genre of songs among the correct instances of that genre<br />
<br />
=== F1-Score: ===<br />
An accuracy metric that combines the classifier’s precision and recall scores by taking the harmonic mean between the two metrics:<br />
<br />
[[File:F1441.png|frame|100px|none|F1-Score]]<br />
<br />
=== Receiver operating characteristics (ROC): ===<br />
* A graphical metric that is used to assess a classification model at different classification thresholds <br />
* In the case of a classification threshold of 0.5, this means that if <math>P(Y = k | X = x) > 0.5</math> then we classify this instance as class k<br />
* Plots the true positive rate versus false positive rate as the classification threshold is varied<br />
<br />
[[File:ROCGraph.jpg|thumb|400px|none|ROC Graph. Comparison of True Positive Rate and False Positive Rate]]<br />
<br />
=== Area Under the Curve (AUC) ===<br />
AUC is the area under the ROC in doing so, the ROC provides an aggregate measure across all possible classification thresholds.<br />
<br />
In the context of the paper: When scoring all songs as <math>Prob(Classical | X=x)</math>, it is the probability that the model ranks a random Classical song at a higher probability than a random non-Classical song.<br />
<br />
[[File:AUCGraph.jpg|thumb|400px|none|Area under the ROC curve.]]<br />
<br />
== Results ==<br />
=== Accuracy Metrics ===<br />
The table below is the accuracy metrics with the classification threshold of 0.5.<br />
<br />
[[File:TruePositiveChart.jpg|thumb|none|True Positive / False Positive Chart]]<br />
On average, CRNN outperforms CNN in true positive and false positive cases. In addition, it is very apparent that false positives are much more frequent for songs in the Instrumental genre, perhaps indicating that more pre-processing needs to be done for songs in this genre or that it should be excluded from analysis completely given how most music has instrumental components.<br />
<br />
<br />
[[File:F1Chart441.jpg|thumb|400px|none|F1 Chart]]<br />
On average, CRNN outperforms CNN in F1-score. <br />
<br />
<br />
[[File:AUCChart.jpg|thumb|400px|none|AUC Chart]]<br />
On average, CRNN also outperforms CNN in AUC metric.<br />
<br />
<br />
CRNN models that consider the frequency features and time sequence patterns of songs have a better classification performance through metrics such as F1 score and AUC when comparing to CNN classifier.<br />
<br />
=== Evaluation of Music Recommendation System: ===<br />
<br />
* A listening experiment was performed with 30 participants to access user responses to given music recommendations.<br />
* Participants choose 5 pieces of music they enjoyed and the recommender system generated 5 new recommendations. The participants then evaluated the music recommendation by recording whether the song was liked or disliked.<br />
* The recommendation system takes two approaches to the recommendation:<br />
** Method one uses only the value of cosine similarity.<br />
** Method two uses the value of cosine similarity and information on music genre.<br />
*Perform test of significance of differences in average user likes between the two methods using a t-statistic:<br />
[[File:H0441.png|frame|100px|none|Hypothesis test between method 1 and method 2]]<br />
<br />
Comparing the two methods, <math> H_0: u_1 - u_2 = 0</math>, we have <math> t_{stat} = -4.743 < -2.037 </math>, which demonstrates that the increase in average user likes with the addition of music genre information is statistically significant.<br />
<br />
== Conclusion: ==<br />
<br />
The two two main conclusions obtained from this paper:<br />
<br />
* The music genre should be a key feature to increase the predictive capabilities of the music recommendation system.<br />
<br />
* To extract the song genre from a song’s audio signals and get overall better performance, CRNN’s are superior to CNN’s as they consider frequency in features and time sequence patterns of audio signals. <br />
<br />
According to the paper, the authors suggested adding other music features like tempo gram for capturing local tempo as a way to improve the accuracy of the recommender system.<br />
<br />
== Critiques/ Insights: ==<br />
# It would be helpful if authors bench-mark their novel approach with other recommendation algorithms such as collaborative filtering to see if there is a lift in predictive capabilities.<br />
# The listening experiment used to evaluate the recommendation system only includes songs that are outputted by the model. Users may be biased if they believe all songs have come from a recommendation system. To remove bias, we suggest having 15 songs where 5 songs are recommended and 10 songs are set. With this in the user’s mind, it may remove some bias in response and give more accurate predictive capabilities. <br />
# It would be better if they go into more details about how CRNN makes it perform better than CNN, in terms of attributes of each network.<br />
# The methodology introduced in this paper is probably also suitable for movie recommendations. As music is presented as spectrograms (images) in a time sequence, and it is very similar to a movie. <br />
# The way of evaluation is a very interesting approach. Since it's usually not easy to evaluate the testing result when it's subjective. By listing all these evaluations' performance, the result would be more comprehensive. A practice that might reduce bias is by coming back to the participants after a couple of days and asking whether they liked the music that was recommended. Often times music "grows" on people and their opinion of a new song may change after some time has passed. <br />
# The paper lacks the comparison between the proposed algorithm and the music recommendation algorithms being used now. It will be clearer to show the superiority of this algorithm.<br />
# The GAN neural network has been proposed to enhance the performance of the neural network, so an improved result may appear after considering using GAN.<br />
# The limitation of CNN and CRNN could be that they are only able to process the spectrograms with single labels rather than multiple labels. This is far from enough for the music recommender systems in today's music industry since the edges between various genres are blurred.<br />
# Is it possible for CNN and CRNN to identify different songs? The model would be harder to train, based on my experience, the efficiency of CNN in R is not very high, which can be improved for future work.<br />
# According to the author, the recommender system is done by calculating the cosine similarity of extraction features from one music to another music. Is possible to represent it by Euclidean distance or p-norm distances?<br />
# In real-life application, most of the music software will have the ability to recommend music to the listener and ask do they like the music that was recommended. It would be a nice application by involving some new information from the listener.<br />
# Actual music listeners do not listen to one genre of music, and in fact listening to the same track or the same genre would be somewhat unusual. Could this method be used to make recommendations not on genre, but based on other categories? (Such as the theme of the lyrics, the pitch of the singer, or the date published). Would this model be able to differentiate between tracks of varying "lyric vocabulation difficulty"? Or would NLP algorithms be needed to consider lyrics?<br />
# This model can be applied to many other fields such as recommending the news in the news app, recommending things to buy in the amazon, recommending videos to watch in YOUTUBE and so on based on the user information.<br />
# Looks like for the most genres, CRNN outperforms CNN, but CNN did do better on a few genres (like Jazz), so it might be better to mix them together or might use CNN for some genres and CRNN for the rest.<br />
# Cosine similarity is used to find songs with similar patterns as the input ones from users. That is, feature variables are extracted from the trained neural network model before the classification layer, and used as the basis to find similar songs. One potential problem of this approach is that if the neural network classifies an input song incorrectly, the extracted feature vector will not be a good representation of the input song. Thus, a song that is in fact really similar to the input song may have a small cosine similarity value, i.e. not be recommended. In conclusion, if the first classification is wrong, future inferences based on that is going to make it deviate further from the true answer. A possible future improvement will be how to offset this inference error.<br />
# In the tables when comparing performance and accuracies of the CNN and CRNN models on different genres of music, the researchers claimed that CRNN had superior performance to CNN models. This seemed intuitive, especially in the cases when the differences in accuracies were large. However, maybe the researchers should consider including some hypothesis testing statistics in such tables, which would support such claims in a more rigorous manner.<br />
# A music recommender system that doesn't use the song's meta data such as artist and genre and rather tries to classify genre itself seems unproductive. I also believe that the specific artist matters much more than the genre since within a genre you have many different styles. It just seems like the authors hamstring their recommender system by excluding other relevant data.<br />
# The genres that are posed in the paper are very broad and may not be specific enough to distinguish a listeners actual tastes (ie, I like rock and roll, but not punk rock, which could both be in the "rock" category). It would be interesting to run similar experiments with more concrete and specific genres to study the possibility of improving accuracy in the model.<br />
# This summary is well organized with detailed explanation to the music recommendation algorithm. However, since the data used in this paper is cleaned to buffer the efficiency of the recommendation, there should be a section evaluating the impact of noise on the performance this algorithm and how to minimize the impact.<br />
# This method will be better if the user choose some certain music genres that they like while doing the sign-up process. This is similar to recommending articles on twitter.<br />
# I have some feedback for the "Evaluation of Music Recommendation System" section. Firstly, there can be a brief mention of the participants' background information. Secondly, the summary mentions that "participants choose 5 pieces of music they enjoyed". Are they free to choose any music they like, or are they choosing from a pool of selections? What are the lengths of these music pieces? Lastly, method one and method two are compared against each other. It's intuitive that method two will outperform method one, since method two makes use of both cosine similarity and information on music genre, whereas method one only makes use of cosine similarity. Thus, saying method two outperforms method one is not necessarily surprising. I would like to see more explanation on why these methods are chosen, and why comparing them directly is considered to be fair.<br />
# It would be better to have more comparison with other existing music recommender system.<br />
# In the Collecting Music Data section, the author has indicated that for maintaining the balance of data for each genre that they are choosing to omit some genres and a portion of the dataset. However, how this was done was not explained explicitly which can be a concern for results replication. It would be better to describe the steps and measures taken to ensure the actions taken by the teams are reproducible. <br />
# For cleaning data, for training purposes, the team is choosing to omit the ones with lower music quality. While this is a sound option, it can be adjusted that the ratings for the music are deducted to adjust the balance. This could be important since a poor music quality could mean either equipment failure or corrupt server storage or it was a recording of a live performance that often does not have a perfect studio quality yet it would be loved by many real-life users. This omission is not entirely justified and feels like a deliberate adjustment for later results.<br />
# It would be more convincing if the author could provide more comparison between CRNN and CNN.<br />
# How is the result used to recommend songs within genres? It looks like it only predicts what genre the user likes to listen and recommends one of the songs from that genre. How can this recommender system be used to recommend songs within the same genre?<br />
# This [https://arxiv.org/pdf/2006.15795.pdf paper] implements CRNN differently; the CNN and RNN are separate and their resulting matrices and combined later. Would using this version of the CRNN potentially improve the accuracy?<br />
# This kind of approach can be used in implementing other recommender systems for, like movies, articles, news, websites etc. It would be helpful if the author could explain and generalize the implementation on other forms of recommender systems.<br />
# The accuracy of the genre classifier seemed really low, considering how distinct the genres sound to humans. The authors recommend adding features to the data but these could likely be extracted from the audio signal. Extra preprocessing would likely go a long way to improve the accuracy.<br />
# Since it was mentioned that different genres were used, it would be interesting to know if the model can classify different languages and how it performs with songs in different languages.<br />
# It is possible to extend this application to classifying baroque, classical, and romantic genre music. This can be beneficial for students (and frankly, people of all ages) who are learning about music. What's even more interesting to see is if this algorithm can distinguish music pieces written by classical musicians such as Beethoven, Haydn, and Mozart.<br />
<br />
== References: ==<br />
Nilashi, M., et.al. ''Collaborative Filtering Recommender Systems''. Research Journal of Applied Sciences, Engineering and Technology 5(16):4168-4182, 2013.<br />
Adiyansjah, Alexander A S Gunawan, Derwin Suhartono, Music Recommender System Based on Genre using Convolutional Recurrent Neural Networks, Procedia Computer Science, https://doi.org/10.1016/j.procs.2019.08.146.</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Music_Recommender_System_Based_using_CRNN&diff=49401Music Recommender System Based using CRNN2020-12-06T16:31:41Z<p>Jcllau: /* Methods and Techniques: */</p>
<hr />
<div>==Introduction and Objective:==<br />
<br />
In the digital era of music streaming, companies, such as Spotify and Pandora, are faced with the following challenge: can they provide users with relevant and personalized music recommendations amidst the ever-growing abundance of music and user data?<br />
<br />
The objective of this paper is to implement a personalized music recommender system that takes user listening history as input and continually finds new music that captures individual user preferences.<br />
<br />
This paper argues that a music recommendation system should vary from the general recommendation system used in practice since it should combine music feature recognition and audio processing technologies to extract music features, and combine them with data on user preferences.<br />
<br />
The authors of this paper took a content-based music approach to build the recommendation system - specifically, comparing the similarity of features based on the audio signal.<br />
<br />
The following two-method approach for building the recommendation system was followed:<br />
#Make recommendations including genre information extracted from classification algorithms.<br />
#Make recommendations without genre information.<br />
<br />
The authors used convolutional recurrent neural networks (CRNN), which is a combination of convolutional neural networks (CNN) and recurrent neural network(RNN), as their main classification model.<br />
<br />
==Methods and Techniques:==<br />
Generally, a music recommender can be divided into three main parts: (i) users, (ii) items, and (iii) user-item matching algorithms. Firstly, a model for a user's music taste is generated based on their profiles. Secondly, item profiling based on editorial, cultural, and acoustic metadata is exploited to increase listener satisfaction. Thirdly, a matching algorithm is employed to recommend personalized music to the listener. Two main approaches are currently available;<br />
<br />
(1) Collaborative filtering<br />
<br />
It is based on users' historical listening data and depends on user ratings. Nearest neighbour is the standard method used for collaborative filtering and can be broken into two classes of methods: (i) user-based neighbourhood methods and (ii) item-based neighbourhood methods. <br />
<br />
User-based neighbourhood methods calculate the similarity between the target user and other users, and selects the k most similar. A weighted average of the most similar users' song ratings is then computed to predict how the target user would rate those songs. Songs that have a high predicted rating are then recommended to the user. In contrast, methods that use item-based neighbourhoods calculate similarities between songs that the target user has rated well and songs they have not listened to in order to recommend songs.<br />
<br />
That being said, collaborative filtering faces many challenges. For example, given that each user sees only a small portion of all music libraries, sparsity and scalability become an issue. However, this can be dealt with using matrix factorization. A more difficult challenge to overcome is the fact that users often don't rate songs when they are listening to music. <br />
<br />
(2) Content-based filtering<br />
<br />
Content based recommendation systems base their recommendations on the similarity of an items features and features that the user has enjoyed. It has two-steps; (i) Extract audio content features and (ii) predict user preferences.<br />
<br />
In this work, the authors take a content-based approach, as they compare the similarity of audio signal features to make recommendations. To classify music, the original music’s audio signal is converted into a spectrogram image. Using the image and the Short Time Fourier Transform (STFT), we convert the data into the Mel scale which is used in the CNN and CRNN models. <br />
=== Mel Scale: === <br />
The scale of pitches that are heard by listeners, which translates to equal pitch increments.<br />
<br />
[[File:Mel.png|frame|none|Mel Scale on Spectrogram]]<br />
<br />
=== Short Time Fourier Transform (STFT): ===<br />
The transformation that determines the sinusoidal frequency of the audio, with a Hanning smoothing function. In the continuous case this is written as: <math>\mathbf{STFT}\{x(t)\}(\tau,\omega) \equiv X(\tau, \omega) = \int_{-\infty}^{\infty} x(t) w(t-\tau) e^{-i \omega t} \, d t </math><br />
<br />
where: <math>w(\tau)</math> is the Hanning smoothing function. The STFT is applied over a specified window length at a certain time allowing the frequency to represented for that given window rather than the entire signal as a typical Fourier Transform would.<br />
<br />
=== Convolutional Neural Network (CNN): ===<br />
A Convolutional Neural Network is a Neural Network that uses convolution in place of matrix multiplication for some layer calculations. By training the data, weights for inputs are updated to find the most significant data relevant to classification. These convolutional layers gather small groups of data with kernels and try to find patterns that can help find features in the overall data. The features are then used for classification. Padding is another technique used to extend the pixels on the edge of the original image to allow the kernel to more accurately capture the borderline pixels. Padding is also used if one wishes the convolved output image to have a certain size. The image on the left represents the mathematical expression of a convolution operation, while the right image demonstrates an application of a kernel on the data.<br />
<br />
[[File:Convolution.png|thumb|400px|left|Convolution Operation]]<br />
[[File:PaddingKernels.png|thumb|400px|center|Example of Padding (white 0s) and Kernels (blue square)]]<br />
<br />
=== Convolutional Recurrent Neural Network (CRNN): === <br />
The CRNN is similar to the architecture of a CNN, but with the addition of a GRU, which is a Recurrent Neural Network (RNN). An RNN is used to treat sequential data, by reusing the activation function of previous nodes to update the output. A Gated Recurrent Unit (GRU) is used to store more long-term memory and will help train the early hidden layers. GRUs can be thought of as LSTMs but with a forget gate, and has fewer parameters than an LSTM. These gates are used to determine how much information from the past should be passed along onto the future. They are originally aimed to prevent the vanishing gradient problem, since deeper networks will result in smaller and smaller gradients at each layer. The GRU can choose to copy over all the information in the past, thus eliminating the risk of vanishing gradients.<br />
<br />
[[File:GRU441.png|thumb|400px|left|Gated Recurrent Unit (GRU)]]<br />
[[File:Recurrent441.png|thumb|400px|center|Diagram of General Recurrent Neural Network]]<br />
<br />
==Data Screening:==<br />
<br />
The authors of this paper used a publicly available music dataset made up of 25,000 30-second songs from the Free Music Archives which contains 16 different genres. The data is cleaned up by removing low audio quality songs, wrongly labelled genres and those that have multiple genres. To ensure a balanced dataset, only 1000 songs each from the genres of classical, electronic, folk, hip-hop, instrumental, jazz and rock were used in the final model. <br />
<br />
[[File:Data441.png|thumb|200px|none|Data sorted by music genre]]<br />
<br />
==Implementation:==<br />
<br />
=== Modeling Neural Networks ===<br />
<br />
As noted previously, both CNNs and CRNNs were used to model the data. The advantage of CRNNs is that they are able to model time sequence patterns in addition to frequency features from the spectrogram, allowing for greater identification of important features. Furthermore, feature vectors produced before the classification stage could be used to improve accuracy. <br />
<br />
In implementing the neural networks, the Mel-spectrogram data was split up into training, validation, and test sets at a ratio of 8:1:1 respectively and labelled via one-hot encoding. This made it possible for the categorical data to be labelled correctly for binary classification. As opposed to classical stochastic gradient descent, the authors opted to use binary classier and ADAM optimization to update weights in the training phase, and parameters of <math>\alpha = 0.001, \beta_1 = 0.9, \beta_2 = 0.999</math>. Binary cross-entropy was used as the loss function. <br />
Input spectrogram image are 96x1366. In both the CNN and CRNN models, the data was trained over 100 epochs and batch size of 50 (limited computing power) with a binary cross-entropy loss function. Notable model specific details are below:<br />
<br />
'''CNN'''<br />
* Five convolutional layers with 3x3 kernel, stride 1, padding, batch normalization, and ReLU activation<br />
* Max pooling layers <br />
* The sigmoid function was used as the output layer<br />
<br />
'''CRNN'''<br />
* Four convolutional layers with 3x3 kernel (which construct a 2D temporal pattern - two layers of RNNs with Gated Recurrent Units), stride 1, padding, batch normalization, ReLU activation, and dropout rate 0.1<br />
* Feature maps are N x1x15 (N = number of features maps, 68 feature maps in this case) is used for RNNs.<br />
* 4 Max pooling layers for four convolutional layers with kernel ((2x2)-(3x3)-(4x4)-(4x4)) and same stride<br />
* The sigmoid function was used as the output layer<br />
<br />
The CNN and CRNN architecture is also given in the charts below.<br />
<br />
[[File:CNN441.png|thumb|800px|none|Implementation of CNN Model]]<br />
[[File:CRNN441.png|thumb|800px|none|Implementation of CRNN Model]]<br />
<br />
=== Music Recommendation System ===<br />
<br />
The recommendation system is computed by the cosine similarity of the extraction features from the neural network. Each genre will have a song act as a centre point for each class. The final inputs of the trained neural networks will be the feature variables. The featured variables will be used in the cosine similarity to find the best recommendations. <br />
<br />
The values are between [-1,1], where larger values are songs that have similar features. When the user inputs five songs, those songs become the new inputs in the neural networks and the features are used by the cosine similarity with other music. The largest five cosine similarities are used as recommendations.<br />
[[File:Cosine441.png|frame|100px|none|Cosine Similarity]]<br />
<br />
== Evaluation Metrics ==<br />
=== Precision: ===<br />
* The proportion of True Positives with respect to the '''predicted''' positive cases (true positives and false positives)<br />
* For example, out of all the songs that the classifier '''predicted''' as Classical, how many are actually Classical?<br />
* Describes the rate at which the classifier predicts the true genre of songs among those predicted to be of that certain genre<br />
<br />
=== Recall: ===<br />
* The proportion of True Positives with respect to the '''actual''' positive cases (true positives and false negatives)<br />
* For example, out of all the songs that are '''actually''' Classical, how many are correctly predicted to be Classical?<br />
* Describes the rate at which the classifier predicts the true genre of songs among the correct instances of that genre<br />
<br />
=== F1-Score: ===<br />
An accuracy metric that combines the classifier’s precision and recall scores by taking the harmonic mean between the two metrics:<br />
<br />
[[File:F1441.png|frame|100px|none|F1-Score]]<br />
<br />
=== Receiver operating characteristics (ROC): ===<br />
* A graphical metric that is used to assess a classification model at different classification thresholds <br />
* In the case of a classification threshold of 0.5, this means that if <math>P(Y = k | X = x) > 0.5</math> then we classify this instance as class k<br />
* Plots the true positive rate versus false positive rate as the classification threshold is varied<br />
<br />
[[File:ROCGraph.jpg|thumb|400px|none|ROC Graph. Comparison of True Positive Rate and False Positive Rate]]<br />
<br />
=== Area Under the Curve (AUC) ===<br />
AUC is the area under the ROC in doing so, the ROC provides an aggregate measure across all possible classification thresholds.<br />
<br />
In the context of the paper: When scoring all songs as <math>Prob(Classical | X=x)</math>, it is the probability that the model ranks a random Classical song at a higher probability than a random non-Classical song.<br />
<br />
[[File:AUCGraph.jpg|thumb|400px|none|Area under the ROC curve.]]<br />
<br />
== Results ==<br />
=== Accuracy Metrics ===<br />
The table below is the accuracy metrics with the classification threshold of 0.5.<br />
<br />
[[File:TruePositiveChart.jpg|thumb|none|True Positive / False Positive Chart]]<br />
On average, CRNN outperforms CNN in true positive and false positive cases. In addition, it is very apparent that false positives are much more frequent for songs in the Instrumental genre, perhaps indicating that more pre-processing needs to be done for songs in this genre or that it should be excluded from analysis completely given how most music has instrumental components.<br />
<br />
<br />
[[File:F1Chart441.jpg|thumb|400px|none|F1 Chart]]<br />
On average, CRNN outperforms CNN in F1-score. <br />
<br />
<br />
[[File:AUCChart.jpg|thumb|400px|none|AUC Chart]]<br />
On average, CRNN also outperforms CNN in AUC metric.<br />
<br />
<br />
CRNN models that consider the frequency features and time sequence patterns of songs have a better classification performance through metrics such as F1 score and AUC when comparing to CNN classifier.<br />
<br />
=== Evaluation of Music Recommendation System: ===<br />
<br />
* A listening experiment was performed with 30 participants to access user responses to given music recommendations.<br />
* Participants choose 5 pieces of music they enjoyed and the recommender system generated 5 new recommendations. The participants then evaluated the music recommendation by recording whether the song was liked or disliked.<br />
* The recommendation system takes two approaches to the recommendation:<br />
** Method one uses only the value of cosine similarity.<br />
** Method two uses the value of cosine similarity and information on music genre.<br />
*Perform test of significance of differences in average user likes between the two methods using a t-statistic:<br />
[[File:H0441.png|frame|100px|none|Hypothesis test between method 1 and method 2]]<br />
<br />
Comparing the two methods, <math> H_0: u_1 - u_2 = 0</math>, we have <math> t_{stat} = -4.743 < -2.037 </math>, which demonstrates that the increase in average user likes with the addition of music genre information is statistically significant.<br />
<br />
== Conclusion: ==<br />
<br />
The two two main conclusions obtained from this paper:<br />
<br />
* The music genre should be a key feature to increase the predictive capabilities of the music recommendation system.<br />
<br />
* To extract the song genre from a song’s audio signals and get overall better performance, CRNN’s are superior to CNN’s as they consider frequency in features and time sequence patterns of audio signals. <br />
<br />
According to the paper, the authors suggested adding other music features like tempo gram for capturing local tempo as a way to improve the accuracy of the recommender system.<br />
<br />
== Critiques/ Insights: ==<br />
# The authors fail to give reference to the performance of current recommendation algorithms used in the industry; my critique would be for the authors to bench-mark their novel approach with other recommendation algorithms such as collaborative filtering to see if there is a lift in predictive capabilities.<br />
# The listening experiment used to evaluate the recommendation system only includes songs that are outputted by the model. Users may be biased if they believe all songs have come from a recommendation system. To remove bias, we suggest having 15 songs where 5 songs are recommended and 10 songs are set. With this in the user’s mind, it may remove some bias in response and give more accurate predictive capabilities. <br />
# They could go into more details about how CRNN makes it perform better than CNN, in terms of attributes of each network.<br />
# The methodology introduced in this paper is probably also suitable for movie recommendations. As music is presented as spectrograms (images) in a time sequence, and it is very similar to a movie. <br />
# The way of evaluation is a very interesting approach. Since it's usually not easy to evaluate the testing result when it's subjective. By listing all these evaluations' performance, the result would be more comprehensive. A practice that might reduce bias is by coming back to the participants after a couple of days and asking whether they liked the music that was recommended. Often times music "grows" on people and their opinion of a new song may change after some time has passed. <br />
# The paper lacks the comparison between the proposed algorithm and the music recommendation algorithms being used now. It will be clearer to show the superiority of this algorithm.<br />
# The GAN neural network has been proposed to enhance the performance of the neural network, so an improved result may appear after considering using GAN.<br />
# The limitation of CNN and CRNN could be that they are only able to process the spectrograms with single labels rather than multiple labels. This is far from enough for the music recommender systems in today's music industry since the edges between various genres are blurred.<br />
# Is it possible for CNN and CRNN to identify different songs? The model would be harder to train, based on my experience, the efficiency of CNN in R is not very high, which can be improved for future work.<br />
# according to the author, the recommender system is done by calculating the cosine similarity of extraction features from one music to another music. Is possible to represent it by Euclidean distance or p-norm distances?<br />
# In real-life application, most of the music software will have the ability to recommend music to the listener and ask do they like the music that was recommended. It would be a nice application by involving some new information from the listener.<br />
# This paper is very similar to another [https://link.springer.com/chapter/10.1007/978-3-319-46131-1_29 paper], written by Bruce Fewerda and Markus Schedl. Both papers are suggesting methods of building music recommendation systems. However, this paper recommends music based on genre, but the paper written by Fewerda and Schedl suggests a personality-based user modeling for music recommender systems.<br />
# Actual music listeners do not listen to one genre of music, and in fact listening to the same track or the same genre would be somewhat unusual. Could this method be used to make recommendations not on genre, but based on other categories? (Such as the theme of the lyrics, the pitch of the singer, or the date published). Would this model be able to differentiate between tracks of varying "lyric vocabulation difficulty"? Or would NLP algorithms be needed to consider lyrics?<br />
# This model can be applied to many other fields such as recommending the news in the news app, recommending things to buy in the amazon, recommending videos to watch in YOUTUBE and so on based on the user information.<br />
# Looks like for the most genres, CRNN outperforms CNN, but CNN did do better on a few genres (like Jazz), so it might be better to mix them together or might use CNN for some genres and CRNN for the rest.<br />
# Cosine similarity is used to find songs with similar patterns as the input ones from users. That is, feature variables are extracted from the trained neural network model before the classification layer, and used as the basis to find similar songs. One potential problem of this approach is that if the neural network classifies an input song incorrectly, the extracted feature vector will not be a good representation of the input song. Thus, a song that is in fact really similar to the input song may have a small cosine similarity value, i.e. not be recommended. In conclusion, if the first classification is wrong, future inferences based on that is going to make it deviate further from the true answer. A possible future improvement will be how to offset this inference error.<br />
# In the tables when comparing performance and accuracies of the CNN and CRNN models on different genres of music, the researchers claimed that CRNN had superior performance to CNN models. This seemed intuitive, especially in the cases when the differences in accuracies were large. However, maybe the researchers should consider including some hypothesis testing statistics in such tables, which would support such claims in a more rigorous manner.<br />
# A music recommender system that doesn't use the song's meta data such as artist and genre and rather tries to classify genre itself seems unproductive. I also believe that the specific artist matters much more than the genre since within a genre you have many different styles. It just seems like the authors hamstring their recommender system by excluding other relevant data.<br />
# The genres that are posed in the paper are very broad and may not be specific enough to distinguish a listeners actual tastes (ie, I like rock and roll, but not punk rock, which could both be in the "rock" category). It would be interesting to run similar experiments with more concrete and specific genres to study the possibility of improving accuracy in the model.<br />
# This summary is well organized with detailed explanation to the music recommendation algorithm. However, since the data used in this paper is cleaned to buffer the efficiency of the recommendation, there should be a section evaluating the impact of noise on the performance this algorithm and how to minimize the impact.<br />
# This method will be better if the user choose some certain music genres that they like while doing the sign-up process. This is similar to recommending articles on twitter.<br />
# I have some feedback for the "Evaluation of Music Recommendation System" section. Firstly, there can be a brief mention of the participants' background information. Secondly, the summary mentions that "participants choose 5 pieces of music they enjoyed". Are they free to choose any music they like, or are they choosing from a pool of selections? What are the lengths of these music pieces? Lastly, method one and method two are compared against each other. It's intuitive that method two will outperform method one, since method two makes use of both cosine similarity and information on music genre, whereas method one only makes use of cosine similarity. Thus, saying method two outperforms method one is not necessarily surprising. I would like to see more explanation on why these methods are chosen, and why comparing them directly is considered to be fair.<br />
# It would be better to have more comparison with other existing music recommender system.<br />
# In the Collecting Music Data section, the author has indicated that for maintaining the balance of data for each genre that they are choosing to omit some genres and a portion of the dataset. However, how this was done was not explained explicitly which can be a concern for results replication. It would be better to describe the steps and measures taken to ensure the actions taken by the teams are reproducible. <br />
# For cleaning data, for training purposes, the team is choosing to omit the ones with lower music quality. While this is a sound option, it can be adjusted that the ratings for the music are deducted to adjust the balance. This could be important since a poor music quality could mean either equipment failure or corrupt server storage or it was a recording of a live performance that often does not have a perfect studio quality yet it would be loved by many real-life users. This omission is not entirely justified and feels like a deliberate adjustment for later results.<br />
# It would be more convincing if the author could provide more comparison between CRNN and CNN.<br />
# How is the result used to recommend songs within genres? It looks like it only predicts what genre the user likes to listen and recommends one of the songs from that genre. How can this recommender system be used to recommend songs within the same genre?<br />
# This [https://arxiv.org/pdf/2006.15795.pdf paper] implements CRNN differently; the CNN and RNN are separate and their resulting matrices and combined later. Would using this version of the CRNN potentially improve the accuracy?<br />
# This kind of approach can be used in implementing other recommender systems for like movies, articles, news, websites etc. It would be helpful if the author could explain and generalize the implementation on other forms of recommender systems.<br />
# The accuracy of the genre classifier seemed really low, considering how distinct the genres sound to humans. The authors recommend adding features to the data but these could likely be extracted from the audio signal. Extra preprocessing would likely go a long way to improve the accuracy.<br />
# Since it was mentioned that different genres were used, it would be interesting to know if the model can classify different languages and how it performs with songs in different languages.<br />
<br />
== References: ==<br />
Nilashi, M., et.al. ''Collaborative Filtering Recommender Systems''. Research Journal of Applied Sciences, Engineering and Technology 5(16):4168-4182, 2013.<br />
Adiyansjah, Alexander A S Gunawan, Derwin Suhartono, Music Recommender System Based on Genre using Convolutional Recurrent Neural Networks, Procedia Computer Science, https://doi.org/10.1016/j.procs.2019.08.146.</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Deep_Learning_for_Cardiologist-level_Myocardial_Infarction_Detection_in_Electrocardiograms&diff=49264Deep Learning for Cardiologist-level Myocardial Infarction Detection in Electrocardiograms2020-12-05T22:46:44Z<p>Jcllau: /* Critiques */</p>
<hr />
<div><br />
== Presented by ==<br />
<br />
Zihui (Betty) Qin, Wenqi (Maggie) Zhao, Muyuan Yang, Amartya (Marty) Mukherjee<br />
<br />
== Introduction ==<br />
<br />
This paper presents ConvNetQuake, an approach on detecting heart disease from ECG signals by fine-tuning the deep learning neural network. For context, ConvNetQuake is a convolutional neural network, used by Perol, Gharbi, and Denolle [4], for Earthquake detection and location from a single waveform. A deep learning approach was used due to the model's ability to be trained using multiple GPUs and terabyte-sized datasets. This, in turn, creates a model that is robust against noise. The purpose of this paper is to provide detailed analyses of the contributions of the ECG leads on identifying heart disease, to show the use of multiple channels in ConvNetQuake enhances prediction accuracy, and to show that feature engineering is not necessary for any of the training, validation, or testing processes. In this area, the combination of data fusion and machine learning techniques exhibits great promise to healthcare innovation, and the analyses in this paper help further this realization. The benefits of translating knowledge between deep learning and its real-world applications in health are also illustrated.<br />
<br />
== Previous Work and Motivation ==<br />
<br />
The database used in previous works is the Physikalisch-Technische Bundesanstalt (PTB) database, which consists of ECG records. Previous papers used techniques, such as CNN, SVM, K-nearest neighbors, naïve Bayes classification, and ANN. From these instances, the paper observes several shortcomings in the previous papers. The first being the issue that most papers use feature selection on the raw ECG data before training the model. Dabanloo and Attarodi [2] used various techniques such as ANN, K-nearest neighbors, and Naïve Bayes. However, they extracted two features, the T-wave integral and the total integral, to aid in localizing and detecting heart disease. Sharma and Sunkaria [3] used SVM and K-nearest neighbors as their classifier, but extracted various features using stationary wavelet transforms to decompose the ECG signal into sub-bands. The second issue is that papers that do not use feature selection would arbitrarily pick ECG leads for classification without rationale. For example, Liu et al. [1] used a deep CNN that uses 3 seconds of ECG signal from lead II at a time as input. The decision for using lead II compared to the other leads was not explained. <br />
<br />
The issue with feature selection is that it can be time-consuming and impractical with large volumes of data. The second issue with the arbitrary selection of leads is that it does not offer insight into why the lead was chosen and the contributions of each lead in the identification of heart disease. Thus, this paper addresses these two issues through implementing a deep learning model that does not rely on feature selection of ECG data and to quantify the contributions of each ECG and Frank lead in identifying heart disease.<br />
<br />
== Model Architecture ==<br />
<br />
The dataset, which was used to train, validate, and test the neural network models, consists of 549 ECG records taken from 290 unique patients. Each ECG record has a mean length of over 100 seconds.<br />
<br />
This Deep Neural Network model was created by modifying the ConvNetQuake model by adding 1D batch normalization layers; this addition helps to combat overfitting. A second modification that was made was to introduce the use of label smoothing, which can help by discouraging the model from making overconfident predictions. Label smoothing refers to the method of relaxing the confidence on the model's prediction labels. The authors' experiments demonstrated that both of these modifications helped to increase model accuracy. <br />
<br />
During the training stage, a 10-second long two-channel input was fed into the neural network. In order to ensure that the two channels were weighted equally, both channels were normalized. Besides, time invariance was incorporated by selecting the 10-second long segment randomly from the entire signal. <br />
<br />
The input layer is a 10-second long ECG signal. There are 8 hidden layers in this model, each of which consists of a 1D convolution layer with the ReLu activation function followed by a batch normalization layer. The output layer is a one-dimensional layer that uses the Sigmoid activation function.<br />
<br />
This model is trained by using batches of size 10. The learning rate is <math>10^{-4}</math>. The ADAM optimizer is used. The ADAM (adaptive moment estimation) optimizer is a stochastic gradient optimization method that uses adaptive learning rates for the parameters used in the estimating the gradient's first and second moments [5]. In training the model, the dataset is split into a train set, validation set, and test set with ratios 80-10-10.<br />
<br />
During the training process, the model was trained from scratch numerous times to avoid inserting unintended variation into the model by randomly initializing weights.<br />
<br />
The following images gives a visual representation of the model.<br />
<br />
[[File:architecture.png | thumb | center | 1000px | Model Architecture (Gupta et al., 2019)]]<br />
<br />
==Results== <br />
<br />
The paper first uses quantification of accuracies for single channels with 20-fold cross-validation, resulting in the highest individual accuracies: v5, v6, vx, vz, and ii. The researchers further investigated the accuracies for pairs of the top 5 highest individual channels using 20-fold cross-validation. They arrived at the conclusion of highest pairs accuracies to fed into a neural network is lead v6 and lead vz. They then use 100-fold cross validation on v6 and vz pair of channels, then compare outliers based on top 20, top 50 and total 100 performing models, finding that standard deviation is non-trivial and there are few models performed very poorly. <br />
<br />
Next, they discussed 2 factors affecting model performance evaluation: 1） Random train-val-test split might have effects on the performance of the model, but it can be improved by access with a larger data set and further discussion; and 2） random initialization of the weights of the neural network shows little effects on the performance of the model performance evaluation, because of showing high average results with a fixed train-val-test split. <br />
<br />
Comparing with other models in the other 12 papers, the model in this article has the highest accuracy, specificity, and precision. With concerns of patients' records affecting the training accuracy, they used 290 fold patient-wise split, resulting in the same highest accuracy of the pair v6 and vz same as record-wise split. The second best pair was ii and vz, which also contains the vz channel. Combining the two best pair channels into v6, vz, vii ultimately gave the best results over 10 trials which has an average of 97.83% in patient-wise split. Even though the patient-wise split might result in lower accuracy evaluation, however, it still maintains a very high average.<br />
<br />
==Conclusion & Discussion== <br />
<br />
The paper introduced a new architecture for heart condition classification based on raw ECG signals using multiple leads. It outperformed the state-of-art model by a large margin of 1 percent. This study finds that out of the 15 ECG channels(12 conventional ECG leads and 3 Frank Leads), channel v6, vz, and ii contain the most meaningful information for detecting myocardial infarction. Also, recent advances in machine learning can be leveraged to produce a model capable of classifying myocardial infraction with a cardiologist-level success rate. To further improve the performance of the models, access to a larger labeled data set is needed. The PTB database is small. It is difficult to test the true robustness of the model with a relatively small test set. If a larger data set can be found to help correctly identify other heart conditions beyond myocardial infraction, the research group plans to share the deep learning models and develop an open-source, computationally efficient app that can be readily used by cardiologists.<br />
<br />
A detailed analysis of the relative importance of each of the 15 ECG channels indicates that deep learning can identify myocardial infraction by processing only ten seconds of raw ECG data from the v6, vz, and ii leads and reaches a cardiologist-level success rate. Deep learning algorithms may be readily used as commodity software. The neural network model that was originally designed to identify earthquakes may be re-designed and tuned to identify myocardial infarction. Feature engineering of ECG data is not required to identify myocardial infraction in the PTB database. This model only required ten seconds of raw ECG data to identify this heart condition with cardiologist-level performance. Access to a larger database should be provided to deep learning researchers so they can work on detecting different types of heart conditions. Deep learning researchers and the cardiology community can work together to develop deep learning algorithms that provide trustworthy, real-time information regarding heart conditions with minimal computational resources.<br />
<br />
Fourier Transform (such as FFT) can be helpful when dealing with ECG signals. It transforms signals from the time domain to the frequency domain, which means some hidden features in frequency may be discovered.<br />
<br />
A limitation specified by the authors is the lack of labeled data. The use of a small dataset such as PTB makes it difficult to determine the robustness of the model due to the small size of the test set. Given a larger dataset, the model could be tested to see if it generalizes to identify heart conditions other than myocardial infarction.<br />
<br />
==Critiques==<br />
- The lack of large, labelled data sets is often a common problem in most applied deep learning studies. Since the PTB database is as small as you describe it to be, the robustness of the model which may be hard to gauge. There are very likely various other physical factors that may play a role in the study which the deep neural network may not be able to adjust for as well, since health data can be somewhat subjective at times and/or may be somewhat inaccurate, especially if machines are used to measurement. This might mean error was propagated forward in the study.<br />
<br />
- Additionally, there is a risk of confirmation bias, which may occur when a model is self-training, especially given the fact that the training set is small.<br />
<br />
- I feel that the results of deep learning models in medical settings where the consequences of misclassification can be severe should be evaluated by assigning weights to classification. In case if the misclassification can lead to severe consequences, then the network should be trained in such a way that it errs towards safety. For example, in case if heart disease, the consequences will be very high if the system says that there is no heart disease when in fact there is. So, the evaluation metric must be selected carefully.<br />
<br />
- This is a useful and meaningful application topic in machine learning. Using Deep Learning to detect heart disease can be very helpful if it is difficult to detect disease by looking at ECG by humans eys. This model also useful for doing statistics, such as calculating the percentage of people get heart disease. But I think the doctor should not 100% trust the result from the model, it is almost impossible to get 100% accuracy from a model. So, I think double-checking by human eyes is necessary if the result is weird. What is more, I think it will be interesting to discuss more applications in mediccal by using this method, such as detecting the Brainwave diagram to predict a person's mood and to diagnose mental diseases.<br />
<br />
- Compared to the dataset for other topics such as object recognition, the PTB database is pretty small with only 549 ECG records. And these are highly unbiased (Table 1) with 4 records for myocarditis and 148 for myocardial infarction. Medical datasets can only be labeled by specialists. This is why these datasets are related small. It would be great if there will be a larger, more comprehensive dataset.<br />
<br />
- Only results using 20-fold cross validation were presented. It should be shown that the results could be reproduced using a more common number of folds like 5 or 10<br />
<br />
- There are potential issues with the inclusion of Frank leads. From a practitioner standpoint, ECGs taken with Frank leads are less common. This could prevent the use of this technique. Additionally, Frank leads are expressible as a linear combinations of the 12 traditional leads. The authors are not adding any fundamentally new information by including them and their inclusion could be viewed as a form of feature selection (going against the authors' original intentions).<br />
<br />
- It will better if we can see how the model in this paper outperformed those methods that used feature selections. The details of the results are not enough.<br />
<br />
- A new extended dataset for PTB dubbed [https://www.nature.com/articles/s41597-020-0495-6 PTB-XL], has 21837 records. Using this dataset could yield a more accurate result, since the original PTB's small dataset posed limitations on the deep learning model.<br />
<br />
- The paper mentions that it has better results, but by how much? what accuracy did the methods you compared to have? Also, what methods did you compare to? (Authors mentioned feature engineering methods but this is vague) Also how much were the labels smoothed? (i.e. 1 -> 0.99 or 1-> 0.95 for example) How much of a difference did the label smoothing make?<br />
<br />
- It is nice to see that the authors also considered training and testing the model on data via a patient-wise split, which gives more insights towards the cases when a patient has multiple records of diagnosis. Obviously and similar to what other critiques suggested, using a patient-wise split might disadvantage from the lack of training data, given that there are only 290 unique patients in the PTB database. Also, acquiring prior knowledge from professionals about correlations, such as causal relationships, between different diagnoses might be helpful for improving the model.<br />
<br />
- As mentioned above, the dataset is comparably small in the context of machine learning. While on the other hand, each record has a length of roughly 100 seconds, which is significantly large as a single input. Therefore, it might be helpful to apply data augmentation algorithms during data preprocessing sections so that there will be a more reasonable dataset than what we currently have so far, which has a high chance of being biased or overfitted.<br />
<br />
- There are several points from the Model Architecture section that can be improved. It mentions that both 1d batch normalization layers and label smoothing are used to improve the accuracy of the models, based on empirical experiment results. Yet, there's no breakdown of how each of these two method improves the accuracy. So it's left unclear whether each method is significant on its own, or the model simultaneously requires both methods in order to achieve improved accuracy. Some more data can be provided about this. It's mentioned that "models are trained from scratch numerous times." How many times is numerous times? Can we get the exact number? Training time about the models should also be provided. This is because if these models take a long time to train, then training them from scratch every time may cause issues with respect to runtime.<br />
<br />
- The authors should have indicated how much the accuracy has been improved by what method. It is a little unclear that how can we define "better results". Also, this paper could be more clear if they included the details about the Model Architecture such as how it was performed and how long was the training time for the model.<br />
<br />
- The summary is lacking several components such as explanation of model, data-preprocessing, result visualization and such. It is hard to understand how the result improved since there is no comparison. Information about dataset is unclear too, it is not explained well what they are and how they are populated.<br />
<br />
- The authors didn't specify how many epochs the model ran for. A common practice when dealing with small datasets is to run more epochs at the risk of overfitting. However the use of batch normalization (and perhaps the introduction of Dropout layers) aid in preventing the model to overfitting the data or affirming the bias of the dataset so more epochs may have improved performance in this case.<br />
<br />
- It is difficult to justify the effectiveness of deep learning for detecting myocardial infarction in EKG due to the lack of information available on the deep learning structure. Meanwhile, false negatives and false positives must be as close to 0 as possible, therefore the authors should test their algorithm on a variety of datasets before determining if deep learning is effective.<br />
<br />
== References ==<br />
<br />
[1] Na Liu et al. "A Simple and Effective Method for Detecting Myocardial Infarction Based on Deep Convolutional Neural Network". In: Journal of Medical Imaging and Health Informatics (Sept. 2018). doi: 10.1166/jmihi.2018.2463.<br />
<br />
[2] Naser Safdarian, N.J. Dabanloo, and Gholamreza Attarodi. "A New Pattern Recognition Method for Detection and Localization of Myocardial Infarction Using T-Wave Integral and Total Integral as Extracted Features from One Cycle of ECG Signal". In: J. Biomedical Science and Engineering (Aug. 2014). doi: http://dx.doi.org/10.4236/jbise.2014.710081.<br />
<br />
[3] L.D. Sharma and R.K. Sunkaria. "Inferior myocardial infarction detection using stationary wavelet transform and machine learning approach." In: Signal, Image and Video Processing (July 2017). doi: https://doi.org/10.1007/s11760-017-1146-z.<br />
<br />
[4] Perol Thibaut, Gharbi Michaël, and Denolle Marin. "Convolutional neural network for earthquake detection and location". In: Science Advances (Feb. 2018). doi: 10.1126/sciadv.1700578<br />
<br />
[5] Kingma, D. and Ba, J., 2015. Adam: A Method for Stochastic Optimization. In: International Conference for Learning Representations. [online] San Diego: 3rd International Conference for Learning Representations, p.1. Available at: <https://arxiv.org/pdf/1412.6980.pdf> [Accessed 3 December 2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Speech2Face:_Learning_the_Face_Behind_a_Voice&diff=49262Speech2Face: Learning the Face Behind a Voice2020-12-05T22:27:43Z<p>Jcllau: /* Discussion and Critiques */</p>
<hr />
<div>== Presented by == <br />
Ian Cheung, Russell Parco, Scholar Sun, Jacky Yao, Daniel Zhang<br />
<br />
== Introduction ==<br />
This paper presents a deep neural network architecture called Speech2Face. This architecture utilizes millions of Internet/Youtube videos of people speaking to learn the correlation between a voice and the respective face. The model learns the correlations, allowing it to produce facial reconstruction images that capture specific physical attributes, such as a person's age, gender, or ethnicity, through a self-supervised procedure. Namely, the model utilizes the simultaneous occurrence of faces and speech in videos and does not need to model the attributes explicitly. This model explores what types of facial information could be extracted from speech without the constraints of predefined facial characterizations. Without any prior information or accurate classifiers, the reconstructions revealed correlations between craniofacial features and voice in addition to the correlation between dominant features (gender, age, ethnicity, etc.) and voice. The model is evaluated and numerically quantifies how closely the reconstruction, done by the Speech2Face model, resembles the true face images of the respective speakers.<br />
<br />
== Ethical Considerations ==<br />
<br />
The authors note that due to the potential sensitivity of facial information, they have chosen to explicitly state some ethical considerations. The first of which is privacy. The paper states that the method cannot recover the true identity of the face or produce faces of specific individuals, but rather will show average-looking faces. The paper also addresses that there are potential dataset biases that exist for the voice-face correlations, thus the faces may not accurately represent the intended population. Finally, it acknowledges that the model uses demographic categories that are defined by a commercial face attribute classifier.<br />
<br />
== Previous Work ==<br />
With visual and audio signals being so dominant and accessible in our daily life, there has been huge interest in how visual and audio perceptions interact with each other. Arandjelovic and Zisserman [1] leveraged the existing database of mp4 files to learn a generic audio representation to classify whether a video frame and an audio clip correspond to each other. These learned audio-visual representations have been used in a variety of setting, including cross-modal retrieval, sound source localization and sound source separation. This also paved the path for specifically studying the association between faces and voices of agents in the field of computer vision. In particular, cross-modal signals extracted from faces and voices have been proposed as a binary or multi-task classification task and there have been some promising results. Studies have been able to identify active speakers of a video, separate speech from multiple concurrent sources, predict lip motion from speech, and even learn the emotion of the agents based on their voices. Aytar et al. [6] proposed a student-teacher training procedure in which a well established visual recognition model was used to transfer the knowledge obtained in the visual modality to the sound modality, using unlabeled videos.<br />
<br />
Recently, various methods have been suggested to use various audio signals to reconstruct visual information, where the reconstructed subject is subjected to a priori. Notably, Duarte et al. [2] were able to synthesize the exact face images and expression of an agent from speech using a GAN model. A generative adversarial network (GAN) model is one that uses a generator to produce seemingly possible data for training and a discriminator that identifies if the training data is fabricated by the generator or if it is real [7]. This paper instead hopes to recover the dominant and generic facial structure from a speech.<br />
<br />
== Motivation ==<br />
It seems to be a common trait among humans to imagine what some people look like when we hear their voices before we have seen what they look lke. There is a strong connection between speech and appearance, which is a direct result of the factors that affect speech, including age, gender, and facial bone structure. In addition, other voice-appearance correlations stem from the way in which we talk: language, accent, speed, pronunciations, etc. These properties of speech are often common among many different nationalities and cultures, which can, in turn, translate to common physical features among different voices. Namely, from an input audio segment of a person speaking, the method would reconstruct an image of the person’s face in a canonical form (frontal-facing, neutral expression). The goal was to study to what extent people can infer how someone else looks from the way they talk. Rather than predicting a recognizable image of the exact face, the authors are more interested in capturing the dominant facial features.<br />
<br />
== Model Architecture == <br />
<br />
'''Speech2Face model and training pipeline'''<br />
<br />
[[File:ModelFramework.jpg|center]]<br />
<br />
<div style="text-align:center;"> Figure 1. '''Speech2Face model and training pipeline''' </div><br />
<br />
<br />
<br />
The Speech2Face Model used to achieve the desired result consists of two parts - a voice encoder which takes in a spectrogram of speech as input and outputs low dimensional face features, and a face decoder which takes in face features as input and outputs a normalized image of a face (neutral expression, looking forward). Figure 1 gives a visual representation of the pipeline of the entire model, from video input to a recognizable face. The combination of the voice encoder and face decoder results are combined to form an image. The variability in facial expressions, head positions and lighting conditions of the face images creates a challenge to both the design and training of the Speech2Face model. It needs a model to figure out many irrelevant variations in the data, and to implicitly extract important internal representations of faces. To avoid this problem the model is trained to first regress to a low dimensional intermediate representation of the face. <br />
<br />
'''Face Decoder''' <br />
The face decoder itself was taken from previous work The VGG-Face model by Cole et al [3] (a face recognition model that is pretrained on a largescale face database [5] is used to extract a 4069-D face feature from the penultimate layer of the network.) and will not be explored in great detail here, but in essence the facenet model is combined with a single multilayer perceptron layer, the result of which is passed through a convolutional neural network to determine the texture of the image, and a multilayer perception to determine the landmark locations. The face decoder kept the VGG-Face model's dimension and weights. The weights were also trained separately and remained fixed during the voice encoder training. <br />
<br />
'''Voice Encoder Architecture''' <br />
<br />
[[File:VoiceEncoderArch.JPG|center]]<br />
<br />
<div style="text-align:center;"> Table 1: '''Voice encoder architecture''' </div><br />
<br />
<br />
<br />
The voice encoder itself is a convolutional neural network, which transforms the input spectrogram into pseudo face features. The exact architecture is given in Table 1. The model alternates between convolution, ReLU, batch normalization layers, and layers of max-pooling. In each max-pooling layer, pooling is only done along the temporal dimension of the data. This is to ensure that the frequency, an important factor in determining vocal characteristics such as tone, is preserved. In the final pooling layer, an average pooling is applied along the temporal dimension. This allows the model to aggregate information over time and allows the model to be used for input speeches of varying lengths. Two fully connected layers at the end are used to return a 4096-dimensional facial feature output.<br />
<br />
'''Training'''<br />
<br />
The AVSpeech dataset, a large-scale audio-visual dataset is used for the training. AVSpeech dataset is comprised of millions of video segments from Youtube with over 100,000 different people. The training data is composed of educational videos and does not provide an accurate representation of the global population, which will clearly affect the model. Also note that facial features that are irrelevant to speech, like hair color, may be predicted by the model. From each video, a 224x224 pixels image of the face was passed through the face decoder to compute a facial feature vector. Combined with a spectrogram of the audio, a training and test set of 1.7 and 0.15 million entries respectively were constructed.<br />
<br />
The voice encoder is trained in a self-supervised manner. A frame that contains the face is extracted from each video and then inputted to the VGG-Face model to extract the feature vector <math>v_f</math>, the 4096-dimensional facial feature vector given by the face decoder on a single frame from the input video. This provides the supervision signal for the voice-encoder. The feature <math>v_s</math>, the 4096 dimensional facial feature vector from the voice encoder, is trained to predict <math>v_f</math>.<br />
<br />
In order to train this model, a proper loss function must be defined. The L1 norm of the difference between <math>v_s</math> and <math>v_f</math>, given by <math>||v_f - v_s||_1</math>, may seem like a suitable loss function, but in actuality results in unstable results and long training times. Figure 2, below, shows the difference in predicted facial features given by <math>||v_f - v_s||_1</math> and the following loss. Based on the work of Castrejon et al. [4], a loss function is used which penalizes the differences in the last layer of the VGG-Face model <math>f_{VGG}</math>: <math> \mathbb{R}^{4096} \to \mathbb{R}^{2622}</math> and the first layer of face decoder <math>f_{dec}</math> : <math> \mathbb{R}^{4096} \to \mathbb{R}^{1000}</math>. The final loss function is given by: $$L_{total} = ||f_{dec}(v_f) - f_{dec}(v_s)|| + \lambda_1||\frac{v_f}{||v_f||} - \frac{v_s}{||v_s||}||^2_2 + \lambda_2 L_{distill}(f_{VGG}(v_f), f_{VGG}(v_s))$$<br />
This loss penalizes on both the normalized Euclidean distance between the 2 facial feature vectors and the knowledge distillation loss, which is given by: $$L_{distill}(a,b) = -\sum_ip_{(i)}(a)\text{log}p_{(i)}(b)$$ $$p_{(i)}(a) = \frac{\text{exp}(a_i/T)}{\sum_j \text{exp}(a_j/T)}$$ Knowledge distillation is used as an alternative to Cross-Entropy. By recommendation of Cole et al [3], <math> T = 2 </math> was used to ensure a smooth activation. <math>\lambda_1 = 0.025</math> and <math>\lambda_2 = 200</math> were chosen so that magnitude of the gradient of each term with respect to <math>v_s</math> are of similar scale at the <math>1000^{th}</math> iteration.<br />
<br />
<center><br />
[[File:L1vsTotalLoss.png | 700px]]<br />
</center><br />
<br />
<div style="text-align:center;"> Figure 2: '''Qualitative results on the AVSpeech test set''' </div><br />
<br />
== Results ==<br />
<br />
'''Confusion Matrix and Dataset statistics'''<br />
<br />
<center><br />
[[File:Confusionmatrix.png| 600px]]<br />
</center><br />
<br />
<div style="text-align:center;"> Figure 3. '''Facial attribute evaluation''' </div><br />
<br />
<br />
<br />
In order to determine the similarity between the generated images and the ground truth, a commercial service known as Face++ which classifies faces for distinct attributes (such as gender, ethnicity, etc) was used. Figure 3 gives a confusion matrix based on gender, ethnicity, and age. By examining these matrices, it is seen that the Speech2Face model performs very well on gender, only misclassifying 6% of the time. Similarly, the model performs fairly well on ethnicities, especially with white or Asian faces. Although the model performs worse on black and Indian faces, that can be attributed to the vastly unbalanced data, where 50% of the data represented a white face, and 80% represented a white or Asian face. <br />
<br />
'''Feature Similarity'''<br />
<br />
<center><br />
[[File:FeatSim.JPG]]<br />
</center><br />
<br />
<div style="text-align:center;"> Table 2. '''Feature similarity''' </div><br />
<br />
<br />
<br />
Another examination of the result is the similarity of features predicted by the Speech2Face model. The cosine, L1, and L2 distance between the facial feature vector produced by the model and the true facial feature vector from the face decoder were computed, and presented, above, in Table 2. A comparison of facial similarity was also done based on the length of audio input. From the table, it is evident that the 6-second audio produced a lower cosine, L1, and L2 distance, resulting in a facial feature vector that is closer to the ground truth. <br />
<br />
'''S2F -> Face retrieval performance'''<br />
<br />
<center><br />
[[File: Retrieval.JPG]]<br />
</center><br />
<br />
<div style="text-align:center;"> Table 3. '''S2F -> Face retrieval performance''' </div><br />
<br />
<br />
<br />
The performance of the model was also examined on how well it could produce the original image. The R@K metric, also known as retrieval performance by recall at K, measures the probability that the K closest images to the model output includes the correct image of the speaker's face. A higher R@K score indicates better performance. From Table 3, above, we see that both the 3-second and 6-second audio showed significant improvement over random chance, with the 6-second audio performing slightly better.<br />
<br />
'''Additional Observations''' <br />
<br />
Ablation studies were carried out to test the effect of audio duration and batch normalization. It was found that the duration of input audio during the training stage had little effect on convergence speed (comparing 3 and 6-second speech segments), while in the test stage longer input speech yields improvement in reconstruction quality. With respect to batch normalization (BN), it was found that without BN reconstructed faces would converge to an average face, while the inclusion of BN led to results which contained much richer facial features.<br />
<br />
== Conclusion ==<br />
The report presented a novel study of face reconstruction from audio recordings of a person speaking. The model was demonstrated to be able to predict plausible face reconstructions with similar facial features to real images of the person speaking. The problem was addressed by learning to align the feature space of speech to that of a pretrained face decoder. The model was trained on millions of videos of people speaking from YouTube. The model was then evaluated by comparing the reconstructed faces with a commercial facial detection service. The authors believe that facial reconstruction allows a more comprehensive view of voice-face correlation compared to predicting individual features, which may lead to new research opportunities and applications.<br />
<br />
== Discussion and Critiques ==<br />
<br />
There is evidence that the results of the model may be heavily influenced by external factors:<br />
<br />
1. Their method of sampling random YouTube videos resulted in an unbalanced sample in terms of ethnicity. Over half of the samples were white. We also saw a large bias in the model's prediction of ethnicity towards white. The bias in the results shows that the model may be overfitting the training data and puts into question what the performance of the model would be when trained and tested on a balanced dataset. Figure (11) highlights this shortcoming: The same man heard speaking in either English or Chinese was predicted to have a "white" appearance or an "asian" appearance respectively.<br />
<br />
2. The model was shown to infer different face features based on language. This puts into question how heavily the model depends on the spoken language. The paper mentioned the quality of face reconstruction may be affected by uncommon languages, where English is the most popular language on Youtube(training set). Testing a more controlled sample where all speech recording was of the same language may help address this concern to determine the model's reliance on spoken language.<br />
<br />
3. The evaluation of the result is also highly dependent on the Face++ classifiers. Since they compare the age, gender, and ethnicity by running the Face++ classifiers on the original images and the reconstructions to evaluate their model, the model that they create can only be as good as the one they are using to evaluate it. Therefore, any limitations of the Face++ classifier may become a limitation of Speech2Face and may result in a compounding effect on the miss-classification rate.<br />
<br />
4. Figure 4.b shows the AVSpeech dataset statistics. However, it doesn't show the statistics about speakers' ethnicity and the language of the video. If we train the model with a more comprehensive dataset that includes enough Asian/Indian English speakers and native language speakers will this increase the accuracy?<br />
<br />
5. One concern about the source of the training data, i.e. the Youtube videos, is that resolution varies a lot since the videos are randomly selected. That may be the reason why the proposed model performs badly on some certain features. For example, it is hard to tell the age when the resolution is bad because the wrinkles on the face are neglected.<br />
<br />
6. The topic of this project is very interesting, but I highly doubt this model will be practical in real-world problems. Because there are many factors to affect a person's sound in a real-world environment. Sounds such as phone clock, TV, car horn and so on. These sounds will decrease the accuracy of the predicted result of the model.<br />
<br />
7. A lot of information can be obtained from someone's voice, this can potentially be useful for detective work and crime scene investigation. In our world of increasing surveillance, public voice recording is quite common and we can reconstruct images of potential suspects based on their voice. In order for this to be achieved, the model has to be thoroughly trained and tested to avoid false positives as it could have a highly destructive outcome for a falsely convicted suspect.<br />
<br />
8. This is a very interesting topic, and this summary has a good structure for readers. Since this model uses Youtube to train model, but I think one problem is that most of the YouTubers are adult, and many additional reasons make this dataset highly unbalanced. What is more, some people may have a baby voice, this also could affect the performance of the model. But overall, this is a meaningful topic, it might help police to locate the suspects. So it might be interesting to apply this to the police.<br />
<br />
9. In addition, it seems very unlikely that any results coming from this model would ever be held in regard even remotely close to being admissible in court to identify a person of interest until the results are improved and the model can be shown to work in real-world applications. Otherwise, there seems to be very little use for such technology and it could have negative impacts on people if they were to be depicted in an unflattering way by the model based on their voice.<br />
<br />
10. Using voice as a factor of constructing the face is a good idea, but it seems like the data they have will have lots of noise and bias. The voice of a video might not come from the person in the video. There are so many YouTubers adjusting their voices before uploading their video and it's really hard to know whether they adjust their voice. Also, most YouTubers are adults so the model cannot have enough training samples about teenagers and kids.<br />
<br />
11. It would be interesting to see how the performance changes with different face encoding sizes (instead of just 4096-D) and also difference face models (encoder/decoders) to see if better performance can be achieved. Also given that the dataset used was unbalanced, was the dataset used to train the face model the same dataset? or was a different dataset used (the model was pretrained). This could affect the performance of the model as well.<br />
<br />
12. The audio input is transformed into a spectrogram before being used for training. They use STFT with a Hann window of 25 mm, a hop length of 10 ms, and 512 FFT frequency bands. They cite this method from a paper that focuses on speech separation, not speech classification. So, it would be interesting to see if there is a better way to do STFT, possibly with different hyperparameters (eg. different windowing, different number of bands), or if another type of transform (eg. wavelet transform) would have better results.<br />
<br />
13. A easy way to get somewhat balanced data is to duplicate the data that are fewer.<br />
<br />
14. This problem is interesting but is hard to generalize. This algorithm didn't account for other genders and mixed-race. In addition, the face recognition software Face++ introduces bias which can carry forward to Speech2Face algorithm. Face recognition algorithms are known to have higher error rates classifying darker-skinned individuals. Thus, it'll be tough to apply it to real-life scenarios like identifying suspects.<br />
<br />
15. This experiment raises a lot of ethical complications when it comes to possible applications in the real world. Even if this model was highly accurate, the implications of being able to discern a person's racial ethnicity, skin tone, etc. based solely on there voice could play in to inherent biases in the application user and this may end up being an issue that needs to be combatted in future research in this area. Another possible issue is that many people will change their intonation or vocal features based on the context (I'll likely have a different voice pattern in a job interview in terms of projection, intonation, etc. than if I was casually chatting/mumbling with a friend while playing video games for example).<br />
<br />
16. Overall a very interesting topic. I want to talk about the technical challenged raised by using the AVSSpeech dataset for training. The paper acknowledges that the AVSSpeech is unbalanced, and 80% of the data are white and Asians. It also says in the results section that "Our model does not perform on other races due to the imbalance in data". There does not seem to be any effort made in balancing the data. I think that there are definitely some data processing techniques that can be used (filtering, data augmentation, etc) to address the class imbalance problem. Not seeing any of these in the paper is a bit disappointing. Another issue I have noticed is that the model aims to predict an average-looking face from certain gender/racial group from voice input, due to ethical considerations. If we cannot reveal the identify of a person, why don't we predict the gender and race directly? Giving an average-looking face does not seem to be the most helpful.<br />
<br />
17. Very interesting research paper to be studied and the main objective was also interesting. This research leads to open question which can be applied to another application such as predicting person's face using voice and can be used in more advanced way. The only risk is how the data is obtained from YouTube where data is not consistent.<br />
<br />
18. The essay uses millions of natural videos of people speaking to find the correlation between face and voice. Since face and voice are commonly used as the identity of a person, there are many possible research opportunities and applications about improving voice and face unlock.<br />
<br />
19. It would be better to have a future work section to discuss the current shortage and explore the possible improvement and applications in the future.<br />
<br />
20. While the idea behind Speech2Face is interesting, ethnic profiling is a huge concern and it can further lead to racial discrimination, racism etc. Developers must put more care and thought into applying Speech2Face in tech before deploying the products.<br />
<br />
== References ==<br />
[1] R. Arandjelovic and A. Zisserman. Look, listen and learn. In<br />
IEEE International Conference on Computer Vision (ICCV),<br />
2017.<br />
<br />
[2] A. Duarte, F. Roldan, M. Tubau, J. Escur, S. Pascual, A. Salvador, E. Mohedano, K. McGuinness, J. Torres, and X. Giroi-Nieto. Wav2Pix: speech-conditioned face generation using generative adversarial networks. In IEEE International<br />
Conference on Acoustics, Speech and Signal Processing<br />
(ICASSP), 2019.<br />
<br />
[3] F. Cole, D. Belanger, D. Krishnan, A. Sarna, I. Mosseri, and W. T. Freeman. Synthesizing normalized faces from facial identity features. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017.<br />
<br />
[4] L. Castrejon, Y. Aytar, C. Vondrick, H. Pirsiavash, and A. Torralba. Learning aligned cross-modal representations from weakly aligned data. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016.<br />
<br />
[5] O. M. Parkhi, A. Vedaldi, and A. Zisserman. Deep face recognition. In British Machine Vision Conference (BMVC), 2015.<br />
<br />
[7] “Overview of GAN Structure | Generative Adversarial Networks,” ''Google Developers'', 24-May-2019. [Online]. Available: https://developers.google.com/machine-learning/gan/gan_structure. [Accessed: 02-Dec-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Semantic_Relation_Classification%E2%80%94%E2%80%94via_Convolution_Neural_Network&diff=47119Semantic Relation Classification——via Convolution Neural Network2020-11-28T01:09:33Z<p>Jcllau: /* Algorithm */</p>
<hr />
<div><br />
<br />
<br />
== Presented by ==<br />
Rui Gong, Xinqi Ling, Di Ma,Xuetong Wang<br />
<br />
== Introduction ==<br />
One of the emerging trends of natural language technologies is their use for the humanities and sciences (Gbor et al., 2018). SemEval 2018 Task 7 mainly solves the problem of relation extraction and classification of two entities in the same sentence into 6 potential relations. The 6 relations are USAGE, RESULT, MODEL-FEATURE, PART WHOLE, TOPIC, and COMPARE.<br />
<br />
SemEval 2018 Task 7 extracted data from 350 scientific paper abstracts, which has 1228 and 1248 annotated sentences for two tasks, respectively. For each data, an example sentence was chosen with its right and left sentences, as well as an indicator showing whether the relation is reserved, then a prediction is made. <br />
<br />
Three models were used for the prediction: Linear Classifiers, Long Short-Term Memory(LSTM), and Convolutional Neural Networks (CNN). In the end, the prediction based on the CNN model was finally submitted since it performed the best among all models. By using the learned custom word embedding function, the research team added a variant of negative sampling, thereby improving performance and surpassing ordinary CNN.<br />
<br />
== Previous Work ==<br />
SemEval 2010 Task 8(Hendrickx et al., 2010) explored the classification of natural language relations and studied the 9 relations between word pairs. However, it is not designed for scientific text analysis, and their challenge differs from the challenge of this paper in its generalizability; this paper’s relations are specific to ACL papers (e.g. MODEL-FEATURE), whereas the 2010 relations are more general, and might necessitate more common-sense knowledge than the 2018 relations. Xu et al. (2015a) and Santos et al. (2015) both applied CNN with negative sampling to finish task7. The 2017 SemEval Task 10 also featured relation extraction within scientific publications.<br />
<br />
== Algorithm ==<br />
<br />
[[File:CNN.png|800px|center]]<br />
<br />
This is the architecture of CNN. We first transform a sentence via Feature embeddings. Basically, we transform each sentence into continuous word embeddings:<br />
<br />
$$<br />
(e^{w_i})<br />
$$<br />
<br />
And word position embeddings:<br />
$$<br />
(e^{wp_i}): e_i = [e^{w_i}, e^{wp_i}]<br />
$$<br />
<br />
In the word embeddings, we got a vocabulary ‘V’, and we will make an embedding word matrix based on the position of the word in the vocabulary. This matrix is trainable and needs to be initialized by pre-trained embedding vectors.<br />
In the word position embeddings, we first need to input some words named ‘entities’ and they are the key for the machine to determine the sentence’s relation. During this process, if we have two entities, we will use the relative position of them in the sentence to make the<br />
embeddings. We will output two vectors and one of them keeps track of the first entity relative position in the sentence ( we will make the entity recorded as 0, the former word recorded as -1 and the next one 1, etc. ). And the same procedure for the second entity. Finally, we will get two vectors concatenated as the position embedding.<br />
<br />
<br />
After the embeddings, the model will transform the embedded sentence to a fix-sized representation of the whole sentence via the convolution layer, finally after the max-pooling to reduce the dimension of the output of the layers, we will get a score for each relation class via a linear transformation.<br />
<br />
<br />
After featurizing all words in the sentence. The sentence of length N can be expressed as a vector of length <math> N </math>, which looks like <br />
$$e=[e_{1},e_{2},\ldots,e_{N}]$$<br />
and each entry represents a token of the word. Also, to apply <br />
convolutional neural network, the subsets of features<br />
$$e_{i:i+j}=[e_{i},e_{i+1},\ldots,e_{i+j}]$$<br />
are given to a weight matrix <math> W\in\mathbb{R}^{(d^{w}+2d^{wp})\times k}</math> to <br />
produce a new feature, defiend as <br />
$$c_{i}=\text{tanh}(W\cdot e_{i:i+k-1}+bias)$$<br />
This process is applied to all subsets of features with length <math> k </math> starting <br />
from the first one. Then a mapped feature factor is produced:<br />
$$c=[c_{1},c_{2},\ldots,c_{N-k+1}]$$<br />
<br />
<br />
The max pooling operation is used, the <math> \hat{c}=max\{c\} </math> was picked.<br />
With different weight filter, different mapped feature vectors can be obtained. Finally, the original <br />
sentence <math> e </math> can be converted into a new representation <math> r_{x} </math> with a fixed length. For example, if there are 5 filters,<br />
then there are 5 features (<math> \hat{c} </math>) picked to create <math> r_{x} </math> for each <math> x </math>.<br />
<br />
Then, the score vector <br />
$$s(x)=W^{classes}r_{x}$$<br />
is obtained which represented the score for each class, given <math> x </math>'s entities' relation will be classified as <br />
the one with the highest score. The <math> W^{classes} </math> here is the model being trained.<br />
<br />
To improve the performance, “Negative Sampling" was used. Given the trained data point <br />
<math> \tilde{x} </math>, and its correct class <math> \tilde{y} </math>. Let <math> I=Y\setminus\{\tilde{y}\} </math> represent the <br />
incorrect labels for <math> x </math>. Basically, the distance between the correct score and the positive margin, and the negative <br />
distance (negative margin plus the second largest score) should be minimized. So the loss function is <br />
$$L=\log(1+e^{\gamma(m^{+}-s(x)_{y})})+\log(1+e^{\gamma(m^{-}-\mathtt{max}_{y'\in I}(s(x)_{y'}))})$$<br />
with margins <math> m_{+} </math>, <math> m_{-} </math>, and penalty scale factor <math> \gamma </math>.<br />
The whole training is based on ACL anthology corpus and there are 25,938 papers with 136,772,370 tokens in total, <br />
and 49,600 of them are unique.<br />
<br />
== Results ==<br />
In machine learning, the most important part is to tune the hyper-parameters. Unlike traditional hyper-parameter optimization, there are some<br />
modifications to the model in order to increase performance on the test set. There are 5 modifications that we can apply:<br />
<br />
'''1.''' Merged Training Sets. It combined two training sets to increase the data set<br />
size and it improves the equality between classes to get better predictions.<br />
<br />
'''2.''' Reversal Indicate Features. It added a binary feature.<br />
<br />
'''3.''' Custom ACL Embeddings. It embedded word vector to an ACL-specific<br />
corps.<br />
<br />
'''4.''' Context words. Within the sentence, it varies in size on a context window<br />
around the entity-enclosed text.<br />
<br />
'''5.''' Ensembling. It used different early stop and random initializations to improve<br />
the predictions.<br />
<br />
These modifications performances well on the training data and they are shown<br />
in table 3.<br />
<br />
[[File:table3.PNG|center]]<br />
<br />
<br />
<br />
As we can see the best choice for this model is ensembling. Because the random initialization made the data more natural and avoided the overfit.<br />
During the training process, there are some methods such that they can only<br />
increase the score on the cross-validation test sets but hurt the performance on<br />
the overall macro-F1 score. Thus, these methods were eventually ruled out.<br />
<br />
<br />
[[File:table4.PNG|center]]<br />
<br />
There are six submissions in total. Three for each training set and the result<br />
is shown in figure 2.<br />
<br />
The best submission for the training set 1.1 is the third submission which did not<br />
use the cross-validation as the test set. Instead, it runs a constant number of<br />
training epochs, and it can be chosen by cross-validation based on the training data. The best submission for the training set 1.2 is the first submission which<br />
extracted 10% of the training data as validation accuracy on the test set predictions.<br />
All in all, early stopping cannot always be based on the accuracy of the validation set<br />
since it cannot guarantee to get better performance on the real test set. Thus,<br />
we have to try new approaches and combine them together to see the prediction<br />
results. Also, doing stratification will certainly improve the performance of<br />
the test data.<br />
<br />
== Conclusions ==<br />
Throughout the process, linear classifiers, sequential random forest, LSTM, and CNN models are tested. Variations are applied to the models. Among all variations, vanilla CNN with negative sampling and ACL-embedding has significantly better performance than all others. Attention-based pooling, up-sampling, and data augmentation are also tested, but they barely perform positive increment on the behavior.<br />
<br />
== Critiques == <br />
<br />
- Applying this in news apps might be beneficial to improve readability by highlighting specific important sections.<br />
<br />
- In the section of previous work, the author mentioned 9 natural language relationships between the word pairs. Among them, 6 potential relationships are USAGE, RESULT, MODEL-FEATURE,PART WHOLE, TOPIC, and COMPARE. It would help the readers to better understand if all 9 relationships are listed in the summary.<br />
<br />
-This topic is interesting and this application might be helpful for some educational websites to improve their website to help readers focus on the important points. I think it will be nice to use Latex to type the equation in the sentence rather than center the equation on the next line. I think it will be interesting to discuss applying this way to other languages such as Chinese, Japanese, etc.<br />
<br />
- It would be a good idea if the authors can provide more details regarding ACL Embeddings and Context words modifications. Scores generated using these two modifications are quite close to the highest Ensembling modification generated score, which makes it a valid consideration to examine these two modifications in detail. <br />
<br />
- This paper is dealing with a similar problem as 'Neural Speed Reading Via Skim-RNN', num 19 paper summary. It will be an interesting approach to compare these two models' performance based on the same dataset.<br />
<br />
- I think it would be highly practical to implement this system as a page-rank system for search engines (such as google, bing, or other platforms like facebook, instagram, etc.) by finding the most prevalent information available in a search query and then matching the search to related text which can be found on webpages. This could also be implemented in search bars on specific websites or locations as well.<br />
<br />
== References ==<br />
Diederik P Kingma and Jimmy Ba. 2014. Adam: A<br />
method for stochastic optimization. arXiv preprint<br />
arXiv:1412.6980.<br />
<br />
DragomirR. Radev, Pradeep Muthukrishnan, Vahed<br />
Qazvinian, and Amjad Abu-Jbara. 2013. The ACL<br />
anthology network corpus. Language Resources<br />
and Evaluation, pages 1–26.<br />
<br />
Tomas Mikolov, Kai Chen, Greg Corrado, and Jeffrey<br />
Dean. 2013a. Efficient estimation of word<br />
representations in vector space. arXiv preprint<br />
arXiv:1301.3781.<br />
<br />
Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado,<br />
and Jeff Dean. 2013b. Distributed representations<br />
of words and phrases and their compositionality.<br />
In Advances in neural information processing<br />
systems, pages 3111–3119.<br />
<br />
Kata Gbor, Davide Buscaldi, Anne-Kathrin Schumann, Behrang QasemiZadeh, Hafa Zargayouna,<br />
and Thierry Charnois. 2018. Semeval-2018 task 7:Semantic relation extraction and classification in scientific papers. <br />
In Proceedings of the 12th International Workshop on Semantic Evaluation (SemEval2018), New Orleans, LA, USA, June 2018.</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Task_Understanding_from_Confusing_Multi-task_Data&diff=47117Task Understanding from Confusing Multi-task Data2020-11-28T01:05:21Z<p>Jcllau: /* Critique */</p>
<hr />
<div>'''Presented By'''<br />
<br />
Qianlin Song, William Loh, Junyue Bai, Phoebe Choi<br />
<br />
= Introduction =<br />
<br />
Narrow AI is an artificial intelligence that outperforms humans in a narrowly defined task. The application of Narrow AI is becoming more and more common. For example, Narrow AI can be used for spam filtering, music recommendation services, and even self-driving cars. However, the widespread use of Narrow AI in important infrastructure functions raises some concerns. Some people think that the characteristics of Narrow AI make it fragile, and when neural networks can be used to control important systems (such as power grids, financial transactions), alternatives may be more inclined to avoid risks. While these machines help companies improve efficiency and cut costs, the limitations of Narrow AI encouraged researchers to look into General AI. <br />
<br />
General AI is a machine that can apply its learning to different contexts, which closely resembles human intelligence. This paper attempts to generalize the multi-task learning system that learns from data from multiple classification tasks. One application is image recognition. In figure 1, an image of an apple corresponds to 3 labels: “red”, “apple” and “sweet”. These labels correspond to 3 different classification tasks: color, fruit, and taste. <br />
<br />
[[File:CSLFigure1.PNG | 500px]]<br />
<br />
Currently, multi-task machines require researchers to construct a task definition. Otherwise, it will end up with different outputs with the same input value. Researchers manually assign tasks to each input in the sample to train the machine. See figure 1(a). This method incurs high annotation costs and restricts the machine’s ability to mirror the human recognition process. This paper is interested in developing an algorithm that understands task concepts and performs multi-task learning without manual task annotations. <br />
<br />
This paper proposed a new learning method called confusing supervised learning (CSL) which includes 2 functions: de-confusing function and mapping function. The first function allocates identifies an input to its respective task and the latter finds the relationship between the input and its label. See figure 1(b). To train a network of CSL, CSL-Net is constructed for representing CSL’s variables. However, this structure cannot be optimized by gradient back-propagation. This difficulty is solved by alternatively performing training for the de-confusing net and mapping net optimization. <br />
<br />
Experiments for function regression and image recognition problems were constructed and compared with multi-task learning with complete information to test CSL-Net’s performance. Experiment results show that CSL-Net can learn multiple mappings for every task simultaneously and achieve the same cognition result as the current multi-task machine sigh complete information.<br />
<br />
= Related Work =<br />
<br />
[[File:CSLFigure2.PNG | 700px]]<br />
<br />
==Multi-task learning==<br />
Multi-task learning aims to learn multiple tasks simultaneously using a shared feature representation. In multi-task learning, the task to which every sample belongs is known. By exploiting similarities and differences between tasks, the learning from one task can improve the learning of another task. (Caruana, 1997) This results in improved learning efficiency. Multi-task learning is used in disciplines like computer vision, natural language processing, and reinforcement learning. In multi-task learning, the task to which every sample belongs is known. With this task definition, the input-output mapping of every task can be represented by a unified function. However, these task definitions are manually constructed, and machines need manual task annotations to learn. Without this annotation, our goal is to understand the task concept from confusing input-label pairs. Overall, It requires manual task annotation to learn and this paper is interested in machine learning without a clear task definition and manual task annotation.<br />
<br />
==Latent variable learning==<br />
Latent variable learning aims to estimate the true function with mixed probability models. See '''figure 2a'''. In the multi-task learning problem without task annotations, samples are generated from multiple distributions instead of one distribution. While, in fact, all input-label pairs come from a unified distribution, and this distribution is estimated by a mixture of multiple probability models. Thus, Due to the lack of task information, latent variable learning is insufficient to solve the research problem, which is multi-task confusing samples.<br />
<br />
==Multi-label learning==<br />
Multi-label learning aims to assign an input to a set of classes/labels. See '''figure 2b'''. It is a generalization of multi-class classification, which classifies an input into one class. In multi-label learning, an input can be classified into more than one class. Unlike multi-task learning, multi-label does not consider the relationship between different label judgments and it is assumed that each judgment is independent. An example where multi-label learning is applicable is the scenario where a website wants to automatically assign applicable tags/categories to an article. Since an article can be related to multiple categories (eg. an article can be tagged under the politics and business categories) multi-label learning is of primary concern here.<br />
<br />
= Confusing Supervised Learning =<br />
<br />
== Description of the Problem ==<br />
<br />
Confusing supervised learning (CSL) offers a solution to the issue at hand. A major area of improvement can be seen in the choice of risk measure. In traditional supervised learning, let <math> (x,y)</math> be the training samples from <math>y=f(x)</math>, which is an identical but unknown mapping relationship. Assuming the risk measure is mean squared error (MSE), the expected risk functional is<br />
<br />
$$ R(g) = \int_x (f(x) - g(x))^2 p(x) \; \mathrm{d}x $$<br />
<br />
where <math>p(x)</math> is the data distribution of the input variable <math>x</math>. In practice, model optimizations are performed using the empirical risk<br />
<br />
$$ R_e(g) = \sum_{i=1}^n (y_i - g(x_i))^2 $$<br />
<br />
When the problem involves different tasks, the model should optimize for each data point depending on the given task. Let <math>f_j(x)</math> be the true ground-truth function for each task <math> j </math>. Therefore, for some input variable <math> x_i </math>, an ideal model <math>g</math> would predict <math> g(x_i) = f_j(x_i) </math>. With this, the risk functional can be modified to fit this new task for traditional supervised learning methods.<br />
<br />
$$ R(g) = \int_x \sum_{j=1}^n (f_j(x) - g(x))^2 p(f_j) p(x) \; \mathrm{d}x $$<br />
<br />
We call <math> (f_j(x) - g(x))^2 p(f_j) </math> the '''confusing multiple mappings'''. Then the optimal solution <math>g^*(x)</math> to the mapping is <math>\bar{f}(x) = \sum_{j=1}^n p(f_j) f_j(x)</math> under this risk functional. However, the optimal solution is not conditional on the specific task at hand but rather on the entire ground-truth functions. Therefore, for every non-trivial set of tasks where <math>f_u(x) \neq f_v(x)</math> for some input <math>x</math> and <math>u \neq v</math>, <math>R(g^*) > 0</math> which implies that there is an unavoidable confusion risk.<br />
<br />
== Learning Functions of CSL ==<br />
<br />
To overcome this issue, the authors introduce two types of learning functions:<br />
* '''Deconfusing function''' &mdash; allocation of which samples come from the same task<br />
* '''Mapping function''' &mdash; mapping relation from input to the output of every learned task<br />
<br />
Suppose there are <math>n</math> ground-truth mappings <math>\{f_j : 1 \leq j \leq n\}</math> that we wish to approximate with a set of mapping functions <math>\{g_k : 1 \leq k \leq l\}</math>. The authors define the deconfusing function as an indicator function <math>h(x, y, g_k) </math> which takes some sample <math>(x,y)</math> and determines whether the sample is assigned to task <math>g_k</math>. Under the CSL framework, the risk functional (mean squared loss) is <br />
<br />
$$ R(g,h) = \int_x \sum_{j,k} (f_j(x) - g_k(x))^2 \; h(x, f_j(x), g_k) \;p(f_j) \; p(x) \;\mathrm{d}x $$<br />
<br />
which can be estimated empirically with<br />
<br />
$$R_e(g,h) = \sum_{i=1}^m \sum_{k=1}^n |y_i - g_k(x_i)|^2 \cdot h(x_i, y_i, g_k) $$<br />
<br />
== Theoretical Results ==<br />
<br />
This novel framework yields some theoretical results to show the viability of its construction.<br />
<br />
'''Theorem 1 (Existence of Solution)'''<br />
''With the confusing supervised learning framework, there is an optimal solution''<br />
$$h^*(x, f_j(x), g_k) = \mathbb{I}[j=k]$$<br />
<br />
$$g_k^*(x) = f_k(x)$$<br />
<br />
''for each <math>k=1,..., n</math> that makes the expected risk function of the CSL problem zero.''<br />
<br />
'''Theorem 2 (Error Bound of CSL)'''<br />
''With probability at least <math>1 - \eta</math> simultaneously with finite VC dimension <math>\tau</math> of CSL learning framework, the risk measure is bounded by<br />
<br />
$$R(\alpha) \leq R_e(\alpha) + \frac{B\epsilon(m)}{2} \left(1 + \sqrt{1 + \frac{4R_e(\alpha)}{B\epsilon(m)}}\right)$$<br />
<br />
''where <math>\alpha</math> is the total parameters of learning functions <math>g, h</math>, <math>B</math> is the upper bound of one sample's risk, <math>m</math> is the size of training data and''<br />
$$\epsilon(m) = 4 \; \frac{\tau (\ln \frac{2m}{\tau} + 1) - \ln \eta / 4}{m}$$<br />
<br />
= CSL-Net =<br />
In this section, the authors describe how to implement and train a network for CSL.<br />
<br />
== The Structure of CSL-Net ==<br />
Two neural networks, deconfusing-net and mapping-net are trained to implement two learning function variables in empirical risk. The optimization target of the training algorithm is:<br />
$$\min_{g, h} R_e = \sum_{i=1}^{m}\sum_{k=1}^{n} (y_i - g_k(x_i))^2 \cdot h(x_i, y_i; g_k)$$<br />
<br />
The mapping-net is corresponding to functions set <math>g_k</math>, where <math>y_k = g_k(x)</math> represents the output of one certain task. The deconfusing-net is corresponding to function h, whose input is a sample <math>(x,y)</math> and output is an n-dimensional one-hot vector. This output vector determines which task the sample <math>(x,y)</math> should be assigned to. The core difficulty of this algorithm is that the risk function cannot be optimized by gradient back-propagation due to the constraint of one-hot output from deconfusing-net. Approximation of softmax will lead the deconfusing-net output into a non-one-hot form, which results in meaningless trivial solutions.<br />
<br />
== Iterative Deconfusing Algorithm ==<br />
To overcome the training difficulty, the authors divide the empirical risk minimization into two local optimization problems. In each single-network optimization step, the parameters of one network are updated while the parameters of another remain fixed. With one network's parameters unchanged, the problem can be solved by a gradient descent method of neural networks. <br />
<br />
'''Training of Mapping-Net''': With function h from deconfusing-net being determined, the goal is to train every mapping function <math>g_k</math> with its corresponding sample <math>(x_i^k, y_i^k)</math>. The optimization problem becomes: <math>\displaystyle \min_{g_k} L_{map}(g_k) = \sum_{i=1}^{m_k} \mid y_i^k - g_k(x_i^k)\mid^2</math>. Back-propagation algorithm can be applied to solve this optimization problem.<br />
<br />
'''Training of Deconfusing-Net''': The task allocation is re-evaluated during the training phase while the parameters of the mapping-net remain fixed. To minimize the original risk, every sample <math>(x, y)</math> will be assigned to <math>g_k</math> that is closest to label y among all different <math>k</math>s. Mapping-net thus provides a temporary solution for deconfusing-net: <math>\hat{h}(x_i, y_i) = arg \displaystyle\min_{k} \mid y_i - g_k(x_i)\mid^2</math>. The optimization becomes: <math>\displaystyle \min_{h} L_{dec}(h) = \sum_{i=1}^{m} \mid {h}(x_i, y_i) - \hat{h}(x_i, y_i)\mid^2</math>. Similarly, the optimization problem can be solved by updating the deconfusing-net with a back-propagation algorithm.<br />
<br />
The two optimization stages are carried out alternately until the solution converges.<br />
<br />
=Experiment=<br />
==Setup==<br />
<br />
3 data sets are used to compare CSL to existing methods, 1 function regression task, and 2 image classification tasks. <br />
<br />
'''Function Regression''': The function regression data comes in the form of <math>(x_i,y_i),i=1,...,m</math> pairs. However, unlike typical regression problems, there are multiple <math>f_j(x),j=1,...,n</math> mapping functions, so the goal is to recover both the mapping functions <math>f_j</math> as well as determine which mapping function corresponds to each of the <math>m</math> observations. 3 scalar-valued, scalar-input functions that intersect at several points with each other have been chosen as the different tasks. <br />
<br />
'''Colorful-MNIST''': The first image classification data set consists of the MNIST digit data that has been colored. Each observation in this modified set consists of a colored image (<math>x_i</math>) and either the color, or the digit it represents (<math>y_i</math>). The goal is to recover the classification task ("color" or "digit") for each observation and construct the 2 classifiers for both tasks. <br />
<br />
'''Kaggle Fashion Product''': This data set has more observations than the "colored-MNIST" data and consists of pictures labeled with either the “Gender”, “Category”, and “Color” of the clothing item.<br />
<br />
==Use of Pre-Trained CNN Feature Layers==<br />
<br />
In the Kaggle Fashion Product experiment, CSL trains fully-connected layers that have been attached to feature-identifying layers from pre-trained Convolutional Neural Networks.<br />
<br />
==Metrics of Confusing Supervised Learning==<br />
<br />
There are two measures of accuracy used to evaluate and compare CSL to other methods, corresponding respectively to the accuracy of the task labeling and the accuracy of the learned mapping function. <br />
<br />
'''Task Prediction Accuracy''': <math>\alpha_T(j)</math> is the average number of times the learned deconfusing function <math>h</math> agrees with the task-assignment ability of humans <math>\tilde h</math> on whether each observation in the data "is" or "is not" in task <math>j</math>.<br />
<br />
$$ \alpha_T(j) = \operatorname{max}_k\frac{1}{m}\sum_{i=1}^m I[h(x_i,y_i;f_k),\tilde h(x_i,y_i;f_j)]$$<br />
<br />
The max over <math>k</math> is taken because we need to determine which learned task corresponds to which ground-truth task.<br />
<br />
'''Label Prediction Accuracy''': <math>\alpha_L(j)</math> again chooses <math>f_k</math>, the learned mapping function that is closest to the ground-truth of task <math>j</math>, and measures its average absolute accuracy compared to the ground-truth of task <math>j</math>, <math>f_j</math>, across all <math>m</math> observations.<br />
<br />
$$ \alpha_L(j) = \operatorname{max}_k\frac{1}{m}\sum_{i=1}^m 1-\dfrac{|g_k(x_i)-f_j(x_i)|}{|f_j(x_i)|}$$<br />
<br />
The purpose of this measure arises from the fact that, in addition to learning mapping allocations like humans, machines should be able to approximate all mapping functions accurately in order to provide corresponding labels. The Label Prediction Accuracy measure captures the exchange equivalence of the following task: each mapping contains its ground-truth output, and machines should be predicting the correct output that is close to the ground-truth. <br />
<br />
==Results==<br />
<br />
Given confusing data, CSL performs better than traditional supervised learning methods, Pseudo-Label(Lee, 2013), and SMiLE(Tan et al., 2017). This is demonstrated by CSL's <math>\alpha_L</math> scores of around 95%, compared to <math>\alpha_L</math> scores of under 50% for the other methods. This supports the assertion that traditional methods only learn the means of all the ground-truth mapping functions when presented with confusing data.<br />
<br />
'''Function Regression''': In order to "correctly" partition the observations into the correct tasks, a 5-shot warm-up was used. In this situation, the CSL methods work well learning the ground-truth. That means the initialization of the neural network is set up properly.<br />
<br />
'''Image Classification''': Visualizations created through Spectral embedding confirm the task labeling proficiency of the deconfusing neural network <math>h</math>.<br />
<br />
The classification and function prediction accuracy of CSL are comparable to supervised learning programs that have been given access to the ground-truth labels.<br />
<br />
==Application of Multi-label Learning==<br />
<br />
CSL also had better accuracy than traditional supervised learning methods, Pseudo-Label(Lee, 2013), and SMiLE(Tan et al., 2017) when presented with partially labelled multi-label data <math>(x_i,y_i)</math>, where <math>y_i</math> is a <math>n</math>-long indicator vector for whether the image <math>(x_i,y_i)</math> corresponds to each of the <math>n</math> labels.<br />
<br />
Applications of multi-label classification include building a recommendation system, social media targeting, as well as detecting adverse drug reaction from text.<br />
<br />
Multi-label can be used to improve the syndrome diagnosis of a patient by focusing on multiple syndromes instead of a single syndrome.<br />
<br />
==Limitations==<br />
<br />
'''Number of Tasks''': The number of tasks is determined by increasing the task numbers progressively and testing the performance. Ideally, a better way of deciding the number of tasks is expected rather than increasing it one by one and seeing which is the minimum number of tasks that gives the smallest risk. Adding low-quality constraints to deconfusing-net is a reasonable solution to this problem.<br />
<br />
'''Learning of Basic Features''': The CSL framework is not good at learning features. So far, a pre-trained CNN backbone is needed for complicated image classification problems. Even though the effectiveness of the proposed algorithm in learning confusing data based on pre-trained features hasn't been affected, the full-connect network can only be trained based on learned CNN features. It is still a challenge for the current algorithm to learn basic features directly through a CNN structure and understand tasks simultaneously.<br />
<br />
= Conclusion =<br />
<br />
This paper proposes the CSL method for tackling the multi-task learning problem with manual task annotations in the input data. The model obtains a basic task concept by differentiating multiple mappings. The paper also demonstrates that the CSL method is an important step to moving from Narrow AI towards General AI for multi-task learning.<br />
<br />
However, there are some limitations that can be improved for future work:<br />
The repeated training process of determining the lowest best task number that has the closest to zero causes inefficiency in the learning process; The current algorithm is difficult to learn basic features directly through the CNN structure, and it is necessary to learn and train a fully connected network based on CNN features in the experiment.<br />
<br />
= Critique =<br />
<br />
The classification accuracy of CSL was made with algorithms not designed to deal with confusing data and which do not first classify the task of each observation.<br />
<br />
Human task annotation is also imperfect, so one additional application of CSL may be to attempt to flag task annotation errors made by humans, such as in sorting comments for items sold by online retailers; concerned customers, in particular, may not correctly label their comments as "refund", "order didn't arrive", "order damaged", "how good the item is" etc.<br />
<br />
This algorithm will also have a huge issue in scaling, as the proposed method requires repeated training processes, so it might be too expensive for researchers to implement and improve on this algorithm.<br />
<br />
This research paper should have included a plot on loss (of both functions) against epochs in the paper. A common issue with fixing the parameters of one network and updating the other is the variability during training. This is prevalent in other algorithms with similar training methods such as generative adversarial networks (GAN). For instance, ''mode collapse'' is the issue of one network stuck in local minima and other networks that rely on this network may receive incorrect signals during backpropagation. In the case of CSL-Net, since the Deconfusing-Net directly relies on Mapping-Net for training labels, if the Mapping-Net is unable to sufficiently converge, the Deconfusing-Net may incorrectly learn the mapping from inputs to the task. For data with high noise, oscillations may severely prolong the time needed for converge because of the strong correlation in prediction between the two networks.<br />
<br />
- It would be interesting to see this implemented in more examples, to test the robustness of different types of data.<br />
<br />
Even though this paper has already included some examples when testing the CSL in experiments, it will be better to include more detailed examples for partial-label in the "Application of Multi-label Learning" section.<br />
<br />
When using this framework for classification, the order of the one-hot classification labels for each task will likely influence the relationships learned between each task, since the same output header is used for all tasks. This may be why this method fails to learn low level representations, and requires pretraining. I would like to see more explanation in the paper about why this isn't a problem, if it was investigated.<br />
<br />
It would be a good idea to include comparison details in the summary to make results and the conclusion more convincing. For instance, though the paper introduced the result generated using confusion data, and provide some applications for multi-label learning, these two sections still fell short and could use some technical details as supporting evidence.<br />
<br />
It is interesting to investigate if the order of adding tasks will influence the model performance.<br />
<br />
It would be an interesting to see the effectiveness of applying CSL in face recognition, such that not only does the algorithm map the face to an identity, it also categorizes the face based on other features like beard/no beard and glasses/no glasses simultaneously.<br />
<br />
= References =<br />
<br />
[1] Su, Xin, et al. "Task Understanding from Confusing Multi-task Data."<br />
<br />
[2] Caruana, R. (1997) "Multi-task learning"<br />
<br />
[3] Lee, D.-H. Pseudo-label: The simple and efficient semi-supervised learning method for deep neural networks. Workshop on challenges in representation learning, ICML, vol. 3, 2013, pp. 2–8. <br />
<br />
[4] Tan, Q., Yu, Y., Yu, G., and Wang, J. Semi-supervised multi-label classification using incomplete label information. Neurocomputing, vol. 260, 2017, pp. 192–202.<br />
<br />
[5] Chavdarova, Tatjana, and François Fleuret. "Sgan: An alternative training of generative adversarial networks." In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 9407-9415. 2018.<br />
<br />
[6] Guo-Ping Liu, Jian-Jun Yan, Yi-Qin Wang, Jing-Jing Fu, Zhao-Xia Xu, Rui Guo, Peng Qian, "Application of Multilabel Learning Using the Relevant Feature for Each Label in Chronic Gastritis Syndrome Diagnosis", Evidence-Based Complementary and Alternative Medicine, vol. 2012, Article ID 135387, 9 pages, 2012. https://doi.org/10.1155/2012/135387</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang&diff=47109User:T358wang2020-11-28T00:15:09Z<p>Jcllau: /* Introduction */</p>
<hr />
<div><br />
== Group ==<br />
Rui Chen, Zeren Shen, Zihao Guo, Taohao Wang<br />
<br />
== Introduction ==<br />
<br />
Landmark recognition is an image retrieval task with its own specific challenges. This paper provides a new and effective method to recognize landmark images, which has been successfully applied to actual images. In this way, statues, buildings, and characteristic objects can be effectively identified.<br />
<br />
There are many difficulties encountered in the development process:<br />
<br />
'''1.''' The first problem is that the concept of landmarks cannot be strictly defined, because landmarks can be any object and building.<br />
<br />
'''2.''' The second problem is that the same landmark can be photographed from different angles. The results of the multi-angle shooting will result in very different picture characteristics. Since the system needs to accurately identify different landmarks, we may also need to consider angles that capture the interior of a building versus the exterior of it. A good model will be able to recognize both.<br />
<br />
'''3.''' The third problem is that the landmark recognition system must recognize a large number of landmarks, and the recognition must achieve high accuracy. The challenge here is that there are significantly more non-landmarks <br />
objects in the real world.<br />
<br />
These problems require that the system should have a very low false alarm rate and high recognition accuracy. <br />
There are also three potential problems:<br />
<br />
'''1.''' The processed data set contains a little error content, the image content is not clean and the quantity is huge.<br />
<br />
'''2.''' The algorithm for learning the training set must be fast and scalable.<br />
<br />
'''3.''' While displaying high-quality judgment landmarks, there is no image geographic information mixed.<br />
<br />
The article describes the deep convolutional neural network (CNN) architecture, loss function, training method, and inference aspects. Using this model, similar metrics to the state of the art model in the test were obtained and the inference time was found to be 15 times faster. Further, because of the efficient architecture, the system can serve in an online fashion. The results of quantitative experiments will be displayed through testing and deployment effect analysis to prove the effectiveness of the model.<br />
<br />
== Related Work ==<br />
<br />
Landmark recognition can be regarded as one of the tasks of image retrieval, and a large number of documents concentrate on image retrieval tasks. In the past two decades, the field of image retrieval has made significant progress, and the main methods can be divided into two categories. <br />
The first is a classic retrieval method using local features, a method based on local feature descriptors organized in bag-of-words(A bag of words model is defined as a simplified representation of the text information by retrieving only the significant words in a sentence or paragraph while disregarding its grammar. The bag of words approach is commonly used in classification tasks where the words are used as features in the model-training), spatial verification, Hamming embedding, and query expansion. These methods are dominant in image retrieval. Later, until the rise of deep convolutional neural networks (CNN), CNNs were used to generate global descriptors of input images.<br />
<br />
Another method is to selectively match the kernel Hamming embedding method extension. With the advent of deep convolutional neural networks, the most effective image retrieval method is based on training CNNs for specific tasks. Deep networks are very powerful for semantic feature representation, which allows us to effectively use them for landmark recognition. This method shows good results but brings additional memory and complexity costs. <br />
The DELF (DEep local feature) by Noh et al. proved promising results. This method combines the classic local feature method with deep learning. This allows us to extract local features from the input image and then use RANSAC for geometric verification. Random Sample Consensus (RANSAC) is a method to smooth data containing a significant percentage of errors, which is ideally suited for applications in automated image analysis where interpretation is based on the data generated by error-prone feature detectors. The goal of the project is to describe a method for accurate and fast large-scale landmark recognition using the advantages of deep convolutional neural networks.<br />
<br />
== Methodology ==<br />
<br />
This section will describe in detail the CNN architecture, loss function, training procedure, and inference implementation of the landmark recognition system. The figure below is an overview of the landmark recognition system.<br />
<br />
[[File:t358wang_landmark_recog_system.png |center|800px]]<br />
<br />
The landmark CNN consists of three parts: the main network, the embedding layer, and the classification layer. To obtain a CNN main network suitable for training landmark recognition model, fine-tuning is applied and several pre-trained backbones (Residual Networks) based on other similar datasets, including ResNet-50, ResNet-200, SE-ResNext-101, and Wide Residual Network (WRN-50-2), are evaluated based on inference quality and efficiency. Based on the evaluation results, WRN-50-2 is selected as the optimal backbone architecture. Fine-tuning is a very efficient technique in various computer vision applications because we can take advantage of everything the model has already learned and applied it to our specific task.<br />
<br />
[[File:t358wang_backbones.png |center|600px]]<br />
<br />
For the embedding layer, as shown in the below figure, the last fully-connected layer after the averaging pool is removed. Instead, a fully-connected 2048 <math>\times</math> 512 layer and a batch normalization are added as the embedding layer. After the batch norm, a fully-connected 512 <math>\times</math> n layer is added as the classification layer. The below figure shows the overview of the CNN architecture of the landmark recognition system.<br />
<br />
[[File:t358wang_network_arch.png |center|800px]]<br />
<br />
To effectively determine the embedding vectors for each landmark class (centroids), the network needs to be trained to have the members of each class to be as close as possible to the centroids. Several suitable loss functions are evaluated including Contrastive Loss, Arcface, and Center loss. The center loss is selected since it achieves the optimal test results and it trains a center of embeddings of each class and penalizes distances between image embeddings as well as their class centers. In addition, the center loss is a simple addition to softmax loss and is trivial to implement.<br />
<br />
When implementing the loss function, a new additional class that includes all non-landmark instances needs to be added and the center loss function needs to be modified as follows: Let n be the number of landmark classes, m be the mini-batch size, <math>x_i \in R^d</math> is the i-th embedding and <math>y_i</math> is the corresponding label where <math>y_i \in</math> {1,...,n,n+1}, n+1 is the label of the non-landmark class. Denote <math>W \in R^{d \times n}</math> as the weights of the classifier layer, <math>W_j</math> as its j-th column. Let <math>c_{y_i}</math> be the <math>y_i</math> th embeddings center from Center loss and <math>\lambda</math> be the balancing parameter of Center loss. Then the final loss function will be: <br />
<br />
[[File:t358wang_loss_function.png |center|600px]]<br />
<br />
In the training procedure, the stochastic gradient descent(SGD) will be used as the optimizer with momentum=0.9 and weight decay = 5e-3. For the center loss function, the parameter <math>\lambda</math> is set to 5e-5. Each image is resized to 256 <math>\times</math> 256 and several data augmentations are applied to the dataset including random resized crop, color jitter, and random flip. The training dataset is divided into four parts based on the geographical affiliation of cities where landmarks are located: Europe/Russia, North America/Australia/Oceania, Middle East/North Africa, and the Far East Regions. <br />
<br />
The paper introduces curriculum learning for landmark recognition, which is shown in the below figure. The algorithm is trained for 30 epochs and the learning rate <math>\alpha_1, \alpha_2, \alpha_3</math> will be reduced by a factor of 10 at the 12th epoch and 24th epoch.<br />
<br />
[[File:t358wang_algorithm1.png |center|600px]]<br />
<br />
In the inference phase, the paper introduces the term “centroids” which are embedding vectors that are calculated by averaging embeddings and are used to describe landmark classes. The calculation of centroids is significant to effectively determine whether a query image contains a landmark. The paper proposes two approaches to help the inference algorithm to calculate the centroids. First, instead of using the entire training data for each landmark, data cleaning is done to remove most of the redundant and irrelevant elements in the image. For example, if the landmark we are interested in is a palace which located on a city square, then images of a similar building on the same square are included in the data which can affect the centroids. Second, since each landmark can have different shooting angles, it is more efficient to calculate a separate centroid for each shooting angle. Hence, a hierarchical agglomerative clustering algorithm is proposed to partition training data into several valid clusters for each landmark and the set of centroids for a landmark L can be represented by <math>\mu_{l_j} = \frac{1}{|C_j|} \sum_{i \in C_j} x_i, j \in 1,...,v</math> where v is the number of valid clusters for landmark L and v=1 if there is no valid clusters for L. <br />
<br />
Once the centroids are calculated for each landmark class, the system can make decisions whether there is any landmark in an image. The query image is passed through the landmark CNN and the resulting embedding vector is compared with all centroids by dot product similarity using approximate k-nearest neighbors (AKNN). To distinguish landmark classes from non-landmark, a threshold <math>\eta</math> is set and it will be compared with the maximum similarity to determine if the image contains any landmarks.<br />
<br />
The full inference algorithm is described in the below figure.<br />
<br />
[[File:t358wang_algorithm2.png |center|600px]]<br />
<br />
We will now look at how the landmark database was created. The collection process was structured by countries, cities and landmarks. They divided the world into several regions: Europe, America, Middle East, Africa, Far East, Australia and Oceania. Within each region, cities were selected that contained a lot of significant landmarks, and some natural landmarks were filtered out as they are difficult to distinguish. Once the cities and landmarks were selected, both images and meta data was collected for each landmark.<br />
<br />
[[File:landmarkcleaning.png | center | 400px]]<br />
<br />
After forming the database, it had to be cleaned before it could be used to train the CNN. First, for each landmark any redundant images were removed. Then for each landmark 5 images were picked that had a high probability of the containing the landmark and were checked manually. The database was then cleaned by parts using the curriculum learning process. It is further described in the pseudocode above. The final database contained 11381 landmarks in 503 cities and 70 countries. With 2331784 landmark images and 900000 non-landmark images. The number of landmarks that have less than 100 images are called "rare".<br />
<br />
== Experiments and Analysis ==<br />
<br />
'''Offline test'''<br />
<br />
In order to measure the quality of the model, an offline test set was collected and manually labeled. According to the calculations, photos containing landmarks make up 1 − 3% of the total number of photos on average. This distribution was emulated in an offline test, and the geo-information and landmark references weren’t used. <br />
The results of this test are presented in the table below. Two metrics were used to measure the results of experiments: Sensitivity — the accuracy of a model on images with landmarks (also called Recall) and Specificity — the accuracy of a model on images without landmarks. Several types of DELF were evaluated, and the best results in terms of sensitivity and specificity were included in the table below. The table also contains the results of the model trained only with Softmax loss, Softmax, and Center loss. Thus, the table below reflects improvements in our approach with the addition of new elements in it.<br />
<br />
[[File:t358wang_models_eval.png |center|600px]]<br />
<br />
It’s very important to understand how a model works on “rare” landmarks due to the small amount of data for them. Therefore, the behavior of the model was examined separately on “rare” and “frequent” landmarks in the table below. The column “Part from total number” shows what percentage of landmark examples in the offline test has the corresponding type of landmarks. And we find that the sensitivity of “frequent” landmarks is much higher than “rare” landmarks.<br />
<br />
[[File:t358wang_rare_freq.png |center|600px]]<br />
<br />
Analysis of the behavior of the model in different categories of landmarks in the offline test is presented in the table below. These results show that the model can successfully work with various categories of landmarks. Predictably better results (92% of sensitivity and 99.5% of specificity) could also be obtained when the offline test with geo-information was launched on the model.<br />
<br />
[[File:t358wang_landmark_category.png |center|600px]]<br />
<br />
'''Revisited Paris dataset'''<br />
<br />
Revisited Paris dataset (RPar)[2] was also used to measure the quality of the landmark recognition approach. This dataset with Revisited Oxford (ROxf) is standard benchmarks for the comparison of image retrieval algorithms. In recognition, it is important to determine the landmark, which is contained in the query image. Images of the same landmark can have different shooting angles or taken inside/outside the building. Thus, it is reasonable to measure the quality of the model in the standard and adapt it to the task settings. That means not all classes from queries are presented in the landmark dataset. For those images containing correct landmarks but taken from different shooting angles within the building, we transferred them to the “junk” category, which does not influence the final score and makes the test markup closer to our model’s goal. Results on RPar with and without distractors in medium and hard modes are presented in the table below. <br />
<br />
<div style="text-align:center;"> '''Revisited Paris Medium''' </div><br />
[[File:t358wang_methods_eval1.png |center|600px]]<br />
<br />
<br />
<div style="text-align:center;"> '''Revisited Paris Hard''' </div><br />
[[File:t358wang_methods_eval2.png |center|600px]]<br />
<br />
== Comparison ==<br />
<br />
Recent most efficient approaches to landmark recognition are built on fine-tuned CNN. We chose to compare our method to DELF on how well each performs on recognition tasks. A brief summary is given below:<br />
<br />
[[File:t358wang_comparison.png |center|600px]]<br />
<br />
''' Offline test and timing '''<br />
<br />
Both approaches obtained similar results for image retrieval in the offline test (shown in the sensitivity&specificity table), but the proposed approach is much faster on the inference stage and more memory efficient.<br />
<br />
To be more detailed, during the inference stage, DELF needs more forward passes through CNN, has to search the entire database, and performs the RANSAC method for geometric verification. All of them make it much more time-consuming than our proposed approach. Our approach mainly uses centroids, this makes it take less time and needs to store fewer elements.<br />
<br />
== Conclusion ==<br />
<br />
In this paper we were hoping to solve some difficulties that emerge when trying to apply landmark recognition to the production level: there might not be a clean & sufficiently large database for interesting tasks, algorithms should be fast, scalable, and should aim for low FP and high accuracy.<br />
<br />
While aiming for these goals, we presented a way of cleaning landmark data. And most importantly, we introduced the usage of embeddings of deep CNN to make recognition fast and scalable, trained by curriculum learning techniques with modified versions of Center loss. Compared to the state-of-the-art methods, this approach shows similar results but is much faster and suitable for implementation on a large scale.<br />
<br />
== Critique ==<br />
The paper selected 5 images per landmark and checked them manually. That means the training process takes a long time on data cleaning and so the proposed algorithm lacks reusability. Also, since only the landmarks that are the largest and most popular were used to train the CNN, the trained model will probably be most useful in big cities instead of smaller cities with less popular landmarks.<br />
<br />
In addition, researchers often look for reliability and reproducibility. By using a private database and manually labelling it, it lends itself to an array of issues in terms of validity and integrity. Researchers who are looking for such an algorithm will not be able to sufficiently determine if the experiments do actually yield the claimed results. Also, manual labelling by those who are related to the individuals conducting this research also raises the question of conflict of interest. The primary experiment of this paper should be on a public and third-party dataset.<br />
<br />
It might be worth looking into the ability to generalize better. <br />
<br />
This is a very interesting implementation in some specific field. The paper shows a process to analyze the problem and trains the model based on deep CNN implementation. In future work, it would be some practical advice to compare the deep CNN model with other models. By comparison, we might receive a more comprehensive training model for landmark recognization.<br />
<br />
This summary has a good structure and the methodology part is very clear for readers to understand. Using some diagrams for the comparison with other methods is good for visualization for readers. Since the dataset is marked manually, so it is kind of time-consuming for training a model. So it might be interesting to discuss how the famous IT company (i.e. Google etc.) fix this problem.<br />
<br />
It would be beneficial if the authors could provide more explanations regarding the DELF method. Visualization of the differences between DELF and CNN from an algorithm and architecture perspective would be highly significant for the context of this paper.<br />
<br />
One challenge of landmark recognition is large number of classes. It would be good to see the comparison between the proposed model and other models in terms of efficiency.<br />
<br />
The scope of this paper seems to work specifically with some of the most well known landmarks in the world, and many of these landmarks are well known because they are very distinct in how they look. It would be interesting to see how well the model works when classifying different landmarks of similar type (ie, Notre Dame Cathedral vs. St. Paul's Cathedral, etc.). It would also be interesting to see how this model compares with other models in literature, or if this is unique, perhaps the authors could scale this model down to a landmark classification problem (castles, churches, parks, etc.) and compare against other models that way.<br />
<br />
Paper 25 (Loss Function Search in Facial Recognition) also utilizes the softmax loss function in feature discrimination in images. The difference between this paper and paper 25 is that this paper focuses on landmark images, whereas paper 25 is for facial recognition. Despite the slightly different application, both papers prove that importance of using the softmax loss function in feature discrimination, which is pretty neat.<br />
<br />
== References ==<br />
[1] Andrei Boiarov and Eduard Tyantov. 2019. Large Scale Landmark Recognition via Deep Metric Learning. In The 28th ACM International Conference on Information and Knowledge Management (CIKM ’19), November 3–7, 2019, Beijing, China. ACM, New York, NY, USA, 10 pages. https://arxiv.org/pdf/1908.10192.pdf 3357384.3357956<br />
<br />
[2] FilipRadenović,AhmetIscen,GiorgosTolias,YannisAvrithis,andOndřejChum.<br />
2018. Revisiting Oxford and Paris: Large-Scale Image Retrieval Benchmarking.<br />
arXiv preprint arXiv:1803.11285 (2018).</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang&diff=47106User:T358wang2020-11-28T00:14:09Z<p>Jcllau: /* Critique */</p>
<hr />
<div><br />
== Group ==<br />
Rui Chen, Zeren Shen, Zihao Guo, Taohao Wang<br />
<br />
== Introduction ==<br />
<br />
Landmark recognition is an image retrieval task with its own specific challenges. This paper provides a new and effective method to recognize landmark images, which has been successfully applied to actual images. In this way, statues, buildings, and characteristic objects can be effectively identified.<br />
<br />
There are many difficulties encountered in the development process:<br />
<br />
'''1.''' The first problem is that the concept of landmarks cannot be strictly defined, because landmarks can be any object and building.<br />
<br />
'''2.''' The second problem is that the same landmark can be photographed from different angles. The results of the multi-angle shooting will result in very different picture characteristics. But the system needs to accurately identify different landmarks. We may also need to consider angles that capture the interior of a building versus the exterior of it, a good model will be able to recognize both.<br />
<br />
'''3.''' The third problem is that the landmark recognition system must recognize a large number of landmarks, and the recognition must achieve high accuracy. The challenge here is that there are significantly more non-landmarks <br />
objects in the real world.<br />
<br />
These problems require that the system should have a very low false alarm rate and high recognition accuracy. <br />
There are also three potential problems:<br />
<br />
'''1.''' The processed data set contains a little error content, the image content is not clean and the quantity is huge.<br />
<br />
'''2.''' The algorithm for learning the training set must be fast and scalable.<br />
<br />
'''3.''' While displaying high-quality judgment landmarks, there is no image geographic information mixed.<br />
<br />
The article describes the deep convolutional neural network (CNN) architecture, loss function, training method, and inference aspects. Using this model, similar metrics to the state of the art model in the test were obtained and the inference time was found to be 15 times faster. Further, because of the efficient architecture, the system can serve in an online fashion. The results of quantitative experiments will be displayed through testing and deployment effect analysis to prove the effectiveness of the model.<br />
<br />
== Related Work ==<br />
<br />
Landmark recognition can be regarded as one of the tasks of image retrieval, and a large number of documents concentrate on image retrieval tasks. In the past two decades, the field of image retrieval has made significant progress, and the main methods can be divided into two categories. <br />
The first is a classic retrieval method using local features, a method based on local feature descriptors organized in bag-of-words(A bag of words model is defined as a simplified representation of the text information by retrieving only the significant words in a sentence or paragraph while disregarding its grammar. The bag of words approach is commonly used in classification tasks where the words are used as features in the model-training), spatial verification, Hamming embedding, and query expansion. These methods are dominant in image retrieval. Later, until the rise of deep convolutional neural networks (CNN), CNNs were used to generate global descriptors of input images.<br />
<br />
Another method is to selectively match the kernel Hamming embedding method extension. With the advent of deep convolutional neural networks, the most effective image retrieval method is based on training CNNs for specific tasks. Deep networks are very powerful for semantic feature representation, which allows us to effectively use them for landmark recognition. This method shows good results but brings additional memory and complexity costs. <br />
The DELF (DEep local feature) by Noh et al. proved promising results. This method combines the classic local feature method with deep learning. This allows us to extract local features from the input image and then use RANSAC for geometric verification. Random Sample Consensus (RANSAC) is a method to smooth data containing a significant percentage of errors, which is ideally suited for applications in automated image analysis where interpretation is based on the data generated by error-prone feature detectors. The goal of the project is to describe a method for accurate and fast large-scale landmark recognition using the advantages of deep convolutional neural networks.<br />
<br />
== Methodology ==<br />
<br />
This section will describe in detail the CNN architecture, loss function, training procedure, and inference implementation of the landmark recognition system. The figure below is an overview of the landmark recognition system.<br />
<br />
[[File:t358wang_landmark_recog_system.png |center|800px]]<br />
<br />
The landmark CNN consists of three parts: the main network, the embedding layer, and the classification layer. To obtain a CNN main network suitable for training landmark recognition model, fine-tuning is applied and several pre-trained backbones (Residual Networks) based on other similar datasets, including ResNet-50, ResNet-200, SE-ResNext-101, and Wide Residual Network (WRN-50-2), are evaluated based on inference quality and efficiency. Based on the evaluation results, WRN-50-2 is selected as the optimal backbone architecture. Fine-tuning is a very efficient technique in various computer vision applications because we can take advantage of everything the model has already learned and applied it to our specific task.<br />
<br />
[[File:t358wang_backbones.png |center|600px]]<br />
<br />
For the embedding layer, as shown in the below figure, the last fully-connected layer after the averaging pool is removed. Instead, a fully-connected 2048 <math>\times</math> 512 layer and a batch normalization are added as the embedding layer. After the batch norm, a fully-connected 512 <math>\times</math> n layer is added as the classification layer. The below figure shows the overview of the CNN architecture of the landmark recognition system.<br />
<br />
[[File:t358wang_network_arch.png |center|800px]]<br />
<br />
To effectively determine the embedding vectors for each landmark class (centroids), the network needs to be trained to have the members of each class to be as close as possible to the centroids. Several suitable loss functions are evaluated including Contrastive Loss, Arcface, and Center loss. The center loss is selected since it achieves the optimal test results and it trains a center of embeddings of each class and penalizes distances between image embeddings as well as their class centers. In addition, the center loss is a simple addition to softmax loss and is trivial to implement.<br />
<br />
When implementing the loss function, a new additional class that includes all non-landmark instances needs to be added and the center loss function needs to be modified as follows: Let n be the number of landmark classes, m be the mini-batch size, <math>x_i \in R^d</math> is the i-th embedding and <math>y_i</math> is the corresponding label where <math>y_i \in</math> {1,...,n,n+1}, n+1 is the label of the non-landmark class. Denote <math>W \in R^{d \times n}</math> as the weights of the classifier layer, <math>W_j</math> as its j-th column. Let <math>c_{y_i}</math> be the <math>y_i</math> th embeddings center from Center loss and <math>\lambda</math> be the balancing parameter of Center loss. Then the final loss function will be: <br />
<br />
[[File:t358wang_loss_function.png |center|600px]]<br />
<br />
In the training procedure, the stochastic gradient descent(SGD) will be used as the optimizer with momentum=0.9 and weight decay = 5e-3. For the center loss function, the parameter <math>\lambda</math> is set to 5e-5. Each image is resized to 256 <math>\times</math> 256 and several data augmentations are applied to the dataset including random resized crop, color jitter, and random flip. The training dataset is divided into four parts based on the geographical affiliation of cities where landmarks are located: Europe/Russia, North America/Australia/Oceania, Middle East/North Africa, and the Far East Regions. <br />
<br />
The paper introduces curriculum learning for landmark recognition, which is shown in the below figure. The algorithm is trained for 30 epochs and the learning rate <math>\alpha_1, \alpha_2, \alpha_3</math> will be reduced by a factor of 10 at the 12th epoch and 24th epoch.<br />
<br />
[[File:t358wang_algorithm1.png |center|600px]]<br />
<br />
In the inference phase, the paper introduces the term “centroids” which are embedding vectors that are calculated by averaging embeddings and are used to describe landmark classes. The calculation of centroids is significant to effectively determine whether a query image contains a landmark. The paper proposes two approaches to help the inference algorithm to calculate the centroids. First, instead of using the entire training data for each landmark, data cleaning is done to remove most of the redundant and irrelevant elements in the image. For example, if the landmark we are interested in is a palace which located on a city square, then images of a similar building on the same square are included in the data which can affect the centroids. Second, since each landmark can have different shooting angles, it is more efficient to calculate a separate centroid for each shooting angle. Hence, a hierarchical agglomerative clustering algorithm is proposed to partition training data into several valid clusters for each landmark and the set of centroids for a landmark L can be represented by <math>\mu_{l_j} = \frac{1}{|C_j|} \sum_{i \in C_j} x_i, j \in 1,...,v</math> where v is the number of valid clusters for landmark L and v=1 if there is no valid clusters for L. <br />
<br />
Once the centroids are calculated for each landmark class, the system can make decisions whether there is any landmark in an image. The query image is passed through the landmark CNN and the resulting embedding vector is compared with all centroids by dot product similarity using approximate k-nearest neighbors (AKNN). To distinguish landmark classes from non-landmark, a threshold <math>\eta</math> is set and it will be compared with the maximum similarity to determine if the image contains any landmarks.<br />
<br />
The full inference algorithm is described in the below figure.<br />
<br />
[[File:t358wang_algorithm2.png |center|600px]]<br />
<br />
We will now look at how the landmark database was created. The collection process was structured by countries, cities and landmarks. They divided the world into several regions: Europe, America, Middle East, Africa, Far East, Australia and Oceania. Within each region, cities were selected that contained a lot of significant landmarks, and some natural landmarks were filtered out as they are difficult to distinguish. Once the cities and landmarks were selected, both images and meta data was collected for each landmark.<br />
<br />
[[File:landmarkcleaning.png | center | 400px]]<br />
<br />
After forming the database, it had to be cleaned before it could be used to train the CNN. First, for each landmark any redundant images were removed. Then for each landmark 5 images were picked that had a high probability of the containing the landmark and were checked manually. The database was then cleaned by parts using the curriculum learning process. It is further described in the pseudocode above. The final database contained 11381 landmarks in 503 cities and 70 countries. With 2331784 landmark images and 900000 non-landmark images. The number of landmarks that have less than 100 images are called "rare".<br />
<br />
== Experiments and Analysis ==<br />
<br />
'''Offline test'''<br />
<br />
In order to measure the quality of the model, an offline test set was collected and manually labeled. According to the calculations, photos containing landmarks make up 1 − 3% of the total number of photos on average. This distribution was emulated in an offline test, and the geo-information and landmark references weren’t used. <br />
The results of this test are presented in the table below. Two metrics were used to measure the results of experiments: Sensitivity — the accuracy of a model on images with landmarks (also called Recall) and Specificity — the accuracy of a model on images without landmarks. Several types of DELF were evaluated, and the best results in terms of sensitivity and specificity were included in the table below. The table also contains the results of the model trained only with Softmax loss, Softmax, and Center loss. Thus, the table below reflects improvements in our approach with the addition of new elements in it.<br />
<br />
[[File:t358wang_models_eval.png |center|600px]]<br />
<br />
It’s very important to understand how a model works on “rare” landmarks due to the small amount of data for them. Therefore, the behavior of the model was examined separately on “rare” and “frequent” landmarks in the table below. The column “Part from total number” shows what percentage of landmark examples in the offline test has the corresponding type of landmarks. And we find that the sensitivity of “frequent” landmarks is much higher than “rare” landmarks.<br />
<br />
[[File:t358wang_rare_freq.png |center|600px]]<br />
<br />
Analysis of the behavior of the model in different categories of landmarks in the offline test is presented in the table below. These results show that the model can successfully work with various categories of landmarks. Predictably better results (92% of sensitivity and 99.5% of specificity) could also be obtained when the offline test with geo-information was launched on the model.<br />
<br />
[[File:t358wang_landmark_category.png |center|600px]]<br />
<br />
'''Revisited Paris dataset'''<br />
<br />
Revisited Paris dataset (RPar)[2] was also used to measure the quality of the landmark recognition approach. This dataset with Revisited Oxford (ROxf) is standard benchmarks for the comparison of image retrieval algorithms. In recognition, it is important to determine the landmark, which is contained in the query image. Images of the same landmark can have different shooting angles or taken inside/outside the building. Thus, it is reasonable to measure the quality of the model in the standard and adapt it to the task settings. That means not all classes from queries are presented in the landmark dataset. For those images containing correct landmarks but taken from different shooting angles within the building, we transferred them to the “junk” category, which does not influence the final score and makes the test markup closer to our model’s goal. Results on RPar with and without distractors in medium and hard modes are presented in the table below. <br />
<br />
<div style="text-align:center;"> '''Revisited Paris Medium''' </div><br />
[[File:t358wang_methods_eval1.png |center|600px]]<br />
<br />
<br />
<div style="text-align:center;"> '''Revisited Paris Hard''' </div><br />
[[File:t358wang_methods_eval2.png |center|600px]]<br />
<br />
== Comparison ==<br />
<br />
Recent most efficient approaches to landmark recognition are built on fine-tuned CNN. We chose to compare our method to DELF on how well each performs on recognition tasks. A brief summary is given below:<br />
<br />
[[File:t358wang_comparison.png |center|600px]]<br />
<br />
''' Offline test and timing '''<br />
<br />
Both approaches obtained similar results for image retrieval in the offline test (shown in the sensitivity&specificity table), but the proposed approach is much faster on the inference stage and more memory efficient.<br />
<br />
To be more detailed, during the inference stage, DELF needs more forward passes through CNN, has to search the entire database, and performs the RANSAC method for geometric verification. All of them make it much more time-consuming than our proposed approach. Our approach mainly uses centroids, this makes it take less time and needs to store fewer elements.<br />
<br />
== Conclusion ==<br />
<br />
In this paper we were hoping to solve some difficulties that emerge when trying to apply landmark recognition to the production level: there might not be a clean & sufficiently large database for interesting tasks, algorithms should be fast, scalable, and should aim for low FP and high accuracy.<br />
<br />
While aiming for these goals, we presented a way of cleaning landmark data. And most importantly, we introduced the usage of embeddings of deep CNN to make recognition fast and scalable, trained by curriculum learning techniques with modified versions of Center loss. Compared to the state-of-the-art methods, this approach shows similar results but is much faster and suitable for implementation on a large scale.<br />
<br />
== Critique ==<br />
The paper selected 5 images per landmark and checked them manually. That means the training process takes a long time on data cleaning and so the proposed algorithm lacks reusability. Also, since only the landmarks that are the largest and most popular were used to train the CNN, the trained model will probably be most useful in big cities instead of smaller cities with less popular landmarks.<br />
<br />
In addition, researchers often look for reliability and reproducibility. By using a private database and manually labelling it, it lends itself to an array of issues in terms of validity and integrity. Researchers who are looking for such an algorithm will not be able to sufficiently determine if the experiments do actually yield the claimed results. Also, manual labelling by those who are related to the individuals conducting this research also raises the question of conflict of interest. The primary experiment of this paper should be on a public and third-party dataset.<br />
<br />
It might be worth looking into the ability to generalize better. <br />
<br />
This is a very interesting implementation in some specific field. The paper shows a process to analyze the problem and trains the model based on deep CNN implementation. In future work, it would be some practical advice to compare the deep CNN model with other models. By comparison, we might receive a more comprehensive training model for landmark recognization.<br />
<br />
This summary has a good structure and the methodology part is very clear for readers to understand. Using some diagrams for the comparison with other methods is good for visualization for readers. Since the dataset is marked manually, so it is kind of time-consuming for training a model. So it might be interesting to discuss how the famous IT company (i.e. Google etc.) fix this problem.<br />
<br />
It would be beneficial if the authors could provide more explanations regarding the DELF method. Visualization of the differences between DELF and CNN from an algorithm and architecture perspective would be highly significant for the context of this paper.<br />
<br />
One challenge of landmark recognition is large number of classes. It would be good to see the comparison between the proposed model and other models in terms of efficiency.<br />
<br />
The scope of this paper seems to work specifically with some of the most well known landmarks in the world, and many of these landmarks are well known because they are very distinct in how they look. It would be interesting to see how well the model works when classifying different landmarks of similar type (ie, Notre Dame Cathedral vs. St. Paul's Cathedral, etc.). It would also be interesting to see how this model compares with other models in literature, or if this is unique, perhaps the authors could scale this model down to a landmark classification problem (castles, churches, parks, etc.) and compare against other models that way.<br />
<br />
Paper 25 (Loss Function Search in Facial Recognition) also utilizes the softmax loss function in feature discrimination in images. The difference between this paper and paper 25 is that this paper focuses on landmark images, whereas paper 25 is for facial recognition. Despite the slightly different application, both papers prove that importance of using the softmax loss function in feature discrimination, which is pretty neat.<br />
<br />
== References ==<br />
[1] Andrei Boiarov and Eduard Tyantov. 2019. Large Scale Landmark Recognition via Deep Metric Learning. In The 28th ACM International Conference on Information and Knowledge Management (CIKM ’19), November 3–7, 2019, Beijing, China. ACM, New York, NY, USA, 10 pages. https://arxiv.org/pdf/1908.10192.pdf 3357384.3357956<br />
<br />
[2] FilipRadenović,AhmetIscen,GiorgosTolias,YannisAvrithis,andOndřejChum.<br />
2018. Revisiting Oxford and Paris: Large-Scale Image Retrieval Benchmarking.<br />
arXiv preprint arXiv:1803.11285 (2018).</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Superhuman_AI_for_Multiplayer_Poker&diff=47102Superhuman AI for Multiplayer Poker2020-11-27T23:37:41Z<p>Jcllau: /* Introduction */</p>
<hr />
<div>== Presented by == <br />
Hansa Halim, Sanjana Rajendra Naik, Samka Marfua, Shawrupa Proshasty<br />
<br />
== Introduction ==<br />
<br />
A superintelligence is a hypothetical agent that possesses intelligence far surpassing that of the brightest and most gifted human minds. In the past two decades, most of the superhuman AI that was built can only beat human players in two-player zero-sum games. The most common strategy that the AI uses to beat those games is to find the most optimal Nash equilibrium. A Nash equilibrium is a pair of strategies such that either single-player switching to any ''other'' choice of strategy (while the other player's strategy remains unchanged) will result in a lower payout for the switching player. Intuitively this is similar to a locally optimal strategy for the players but is (i) not guaranteed to exist and (ii) may not be the truly optimal strategy (for example, in the "Prisoner's dilemma" the Nash equilibrium of both players betraying each other is not the optimal strategy).<br />
<br />
More specifically, in the game of poker, we only have AI models that can beat human players in two-player settings. An example of an AI model that can successfully beat two players in poker is Libratus, which is an AI developed in 2017 that also used MCCFR. Poker is a great challenge in AI and game theory because it captures the challenges in hidden information so elegantly. This means that developing a superhuman AI in multiplayer poker is the remaining great milestone in this field, because there is no polynomial-time algorithm that can find a Nash equilibrium in two-player non-zero-sum games, and having one would have surprising implications in computational complexity theory.<br />
<br />
In this paper, the AI which we call Pluribus is capable of defeating human professional poker players in Texas hold'em poker which is a six-player poker game and is the most commonly played format in the world. The algorithm that is used is not guaranteed to converge to a Nash algorithm outside of two-player zero-sum games. However, it uses a strong strategy that is capable of consistently defeating elite human professionals. This shows that despite not having strong theoretical guarantees on performance, they are capable of applying a wider class of superhuman strategies.<br />
<br />
== Nash Equilibrium in Multiplayer Games ==<br />
<br />
Many AI has reached superhuman performance in games like checkers, chess, two-player limit poker, Go, and two-player no-limit poker. Nash equilibrium has been proven to exist in all finite games and numerous infinite games. However, the challenge is to find the equilibrium. It is the best possible strategy and is unbeatable in two-player zero-sum games since it guarantees to not lose in expectation regardless of what the opponent is doing.<br />
<br />
To have a deeper understanding of Nash Equilibria we must first define some basic game theory concepts. The first one being a strategic game, in game theory a strategic game consists of a set of players, for each player a set of actions and for each player preferences (or payoffs) over the set of action profiles (set of combination of actions). With these three elements, we can model a wide variety of situations. Now a Nash Equilibrium is an action profile, with the property that no player can do better by changing their action, given that all other players' actions remain the same. A common illustration of Nash equilibria is the Prisoner's Dilemma. We also have mixed strategies and mixed strategy Nash equilibria. A mixed strategy is when instead of a player choosing an action they apply a probability distribution to their set of actions and pick randomly. Note that with mixed strategies we must look at the expected payoff of the player given the other players' strategies. Therefore a mixed strategy Nash Equilibria involves at least one player playing with a mixed strategy where no player can increase their expected payoff by changing their action, given that all other players' actions remain the same. Then we can define a pure Nash Equilibria to where no one is playing a mixed strategy. We also must be aware that a single game can have multiple pure Nash equilibria and mixed Nash equilibria. Also, Nash Equilibria are purely theoretical and depend on players acting optimally and being rational, this is not always the case with humans and we can act very irrationally. Therefore empirically we will see that games can have very unexpected outcomes and you may be able to get a better payoff if you move away from a strictly theoretical strategy and take advantage of your opponents irrational behavior. <br />
<br />
The insufficiency with current AI systems is that they only try to achieve Nash equilibriums instead of trying to actively detect and exploit weaknesses in opponents. At the Nash equilibrium, there is no incentive for any player to change their initial strategy, so it is a stable state of the system. For example, let's consider the game of Rock-Paper-Scissors, the Nash equilibrium is to randomly pick any option with equal probability. However, we can see that this means the best strategy that the opponent can have will result in a tie. Therefore, in this example, our player cannot win in expectation. Now let's try to combine the Nash equilibrium strategy and opponent exploitation. We can initially use the Nash equilibrium strategy and then change our strategy overtime to exploit the observed weaknesses of our opponent. For example, we switch to always play Rock against our opponent who always plays Scissors. However, by shifting away from the Nash equilibrium strategy, it opens up the possibility for our opponent to use our strategy against ourselves. For example, they notice we always play Rock and thus they will now always play Paper.<br />
<br />
Trying to approximate a Nash equilibrium is hard in theory, and in games with more than two players, it can only find a handful of possible strategies per player. Currently, existing techniques to find ways to exploit an opponent require way too many samples and are not competitive enough outside of small games. Finding a Nash equilibrium in three or more players is a great challenge. Even we can efficiently compute a Nash equilibrium in games with more than two players, it is still highly questionable if playing the Nash equilibrium strategy is a good choice. Additionally, if each player tries to find their own version of a Nash equilibrium, we could have infinitely many strategies and each player’s version of the equilibrium might not even be a Nash equilibrium.<br />
<br />
Consider the Lemonade Stand example from Figure 1 Below. We have 4 players and the goal for each player is to find a spot in the ring that is furthest away from every other player. This way, each lemonade stand can cover as much selling region as possible and generate maximum revenue. In the left circle, we have three different Nash equilibria distinguished by different colors which would benefit everyone. The right circle is an illustration of what would happen if each player decides to calculate their own Nash equilibrium.<br />
<br />
[[File:Lemonade_Example.png| 600px |center ]]<br />
<br />
<div align="center">Figure 1: Lemonade Stand Example</div><br />
<br />
From the right circle in Figure 1, we can see that when each player tries to calculate their own Nash equilibria, their own version of the equilibrium might not be a Nash equilibrium and thus they are not choosing the best possible location. This shows that attempting to find a Nash equilibrium is not the best strategy outside of two-player zero-sum games, and our goal should not be focused on finding a specific game-theoretic solution. Instead, we need to focus on observations and empirical results that consistently defeat human opponents.<br />
<br />
== Theoretical Analysis ==<br />
Pluribus uses forms of abstraction to make computations scalable. To simplify the complexity due to too many decision points, some actions are eliminated from consideration and similar decision points are grouped together and treated as identical. This process is called abstraction. Pluribus uses two kinds of abstraction: Action abstraction and information abstraction. Action abstraction reduces the number of different actions the AI needs to consider. For instance, it does not consider all bet sizes (exact number of bets it considers varies between 1 and 14 depending on the situation). Information abstraction groups together decision points that reveal similar information. For instance, the player’s cards and revealed board cards. This is only used to reason about situations on future betting rounds, never the current betting round.<br />
<br />
Pluribus uses a builtin strategy - “Blueprint strategy”, which it gradually improves by searching in real time in situations it finds itself in during the course of the game. In the first betting round pluribus uses the initial blueprint strategy when the number of decision points is small. The blueprint strategy is computed using Monte Carlo Counterfactual Regret Minimization (MCCFR) algorithm. CFR is commonly used in imperfect information games AI which is trained by repeatedly playing against copies of itself, without any data of human or prior AI play used as input. For ease of computation of CFR in this context, poker is represented <br />
as a game tree. A game tree is a tree structure where each node represents either a player’s decision, a chance event, or a terminal outcome and edges represent actions taken. <br />
<br />
[[File:Screen_Shot_2020-11-17_at_11.57.00_PM.png| 600px |center ]]<br />
<br />
<div align="center">Figure 1: Kuhn Poker (Simpler form of Poker) </div><br />
<br />
At the start of each iteration, MCCFR stimulates a hand of poker randomly (Cards held by a player at a given time) and designates one player as the traverser of the game tree. Once that is completed, the AI reviews the decision made by the traverser at a decision point in the game and investigates whether the decision was profitable. The AI compares its decision with other actions available to the traverser at that point and also with the future hypothetical decisions that would have been made following the other available actions. To evaluate a decision, the Counterfactual Regret factor is used. This is the difference between what the traverser would have expected to receive for choosing an action and actually received on the iteration. Thus regret is a numeric value, where a positive regret indicates you regret your decision, a negative regret indicates you are happy with your decision, and zero regret indicates that you are indifferent.<br />
<br />
The value of counterfactual regret for a decision is adjusted over the iterations as more scenarios or decision points are encountered. This means at the end of each iteration, the traverser’s strategy is updated so actions with higher counterfactual regret is chosen with higher probability. CFR minimizes regret over many iterations until the average strategy overall iterations converges and the average strategy is the approximated Nash equilibrium. CFR guarantees in all finite games that all counterfactual regrets grow sublinearly in the number of iterations. Pluribus uses Linear CFR in early iterations to reduce the influence of initial bad iterations i.e it assigns a weight of T to regret contributions at iteration T. This leads to the strategy improving more quickly in practice.<br />
<br />
An additional feature of Pluribus is that in the subgames, instead of assuming that all players play according to a single strategy, Pluribus considers that each player may choose between k different strategies specialized to each player when a decision point is reached. This results in the searcher choosing a more balanced strategy. For instance, if a player never bluffs while holding the best possible hand then the opponents would learn that fact and always fold in that scenario. To fold in that scenario is a balanced strategy than to bet.<br />
Therefore, the blueprint strategy is produced offline for the entire game and it is gradually improved while making real-time decisions during the game.<br />
<br />
== Experimental Results ==<br />
To test how well Pluribus functions, it was tested against human players in 2 formats. The first format included 5 human players and one copy of Pluribus (5H+1AI). The 13 human participants were poker players who have won more than $1M playing professionally and were provided with cash incentives to play their best. 10,000 hands of poker were played over 12 days with the 5H+1AI format by anonymizing the players by providing each of them with aliases that remained consistent throughout all their games. The aliases helped the players keep track of the tendencies and types of games played by each player over the 10,000 hands played. <br />
<br />
The second format included one human player and 5 copies of Pluribus (1H+5AI) . There were 2 more professional players who split another 10,000 hands of poker by playing 5000 hands each and followed the same aliasing process as the first format.<br />
Performance was measured using milli big blinds per game, mbb/game, (i.e. the initial amount of money the second player has to put in the pot) which is the standard measure in the AI field. Additionally, AIVAT was used as the variance reduction technique to control for luck in the games, and significance tests were run at a 95% significance level with one-tailed t-tests as a check for Pluribus’s performance in being profitable.<br />
<br />
Applying AIVAT the following were the results:<br />
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"<br />
! scope="col" | Format !! scope="col" | Average mbb/game !! scope="col" | Standard Error in mbb/game !! scope="col" | P-value of being profitable <br />
|-<br />
! scope="row" | 5H+1AI <br />
| 48 || 25 || 0.028 <br />
|-<br />
! scope="row" | 1H+5AI <br />
| 32 || 15 || 0.014<br />
|}<br />
[[File:top.PNG| 950px | x450px |left]]<br />
<br />
<br />
<div align="center">"Figure 3. Performance of Pluribus in the 5 humans + 1 AI experiment. The dots show Pluribus's performance at the end of each day of play. (Top) The lines show the win rate (solid line) plus or minus the standard error (dashed lines). (Bottom) The lines show the cumulative number of mbbs won (solid line) plus or minus the standard error (dashed lines). The relatively steady performance of Pluribus over the course of the 10,000-hand experiment also suggests that the humans were unable to find exploitable weaknesses in the bot."</div> <br />
<br />
Optimal play in Pluribus looks different from well-known poker conventions: A standard convention of “limping” in poker (calling the 'big blind' rather than folding or raising) is confirmed to be not optimal by Pluribus since it initially experimented with it but eliminated this from its strategy over its games of self-play. On the other hand, another convention of “donk betting” (starting a round by betting when someone else ended the previous round with a call) that is dismissed by players was adopted by Pluribus much more often than played by humans, and is proven to be profitable.<br />
<br />
== Discussion and Critiques ==<br />
<br />
Pluribus' Blueprint strategy and Abstraction methods effectively reduces the computational power required. Hence it was computed in 8 days and required less than 512 GB of memory, and costs about $144 to produce. This is in sharp contrast to all the other recent superhuman AI milestones for games. This is a great way the researchers have condensed down the problem to fit the current computational powers. <br />
<br />
Pluribus definitely shows that we can capture observational data and empirical results to construct a superhuman AI without requiring theoretical guarantees, this can be a baseline for future AI inventions and help in the research of AI. It would be interesting to use Pluribus's way of using non-theoretical approach in more real life problems such as autonomous driving or stock market trading.<br />
<br />
Extending this idea beyond two player zero sum games will have many applications in real life.<br />
<br />
The summary for Superhuman AI for Multiplayer Poker is very well written, with a detailed explanation of the concept, steps, and result and with a combination of visual images. However, it seems that the experiment of the study is not well designed. For example: sample selection is not strict and well defined, this could cause selection bias introduced into the result and thus making it not generalizable.<br />
<br />
Superhuman AI, while sounding superior, is actually not uncommon. There has been many endeavours on mastering poker such as the Recursive Belief-based Learning (ReBeL) by Facebook Research. They pursued a method of reinforcement learning on partially observable Markov decision process which was inspired by the recent successes of AlphaZero. For Pluribus to demonstrate how effective it is compared to the state-of-the-art, it should run some experiments against ReBeL.<br />
<br />
This is a very interesting topic, and this summary is clear enough for readers to understand. I think this application not only can apply in poker, maybe thinking more applications in other area? There are many famous AI that really changing our life. For example, AlphaGo and AlphaStar, which are developed by Google DeepMind, defeated professional gamers. Discussing more this will be interesting.<br />
<br />
One of the biggest issues when applying AI to games against humans (when not all information is known, ie, opponents cards) is the assumption is generally made that the human players are rational players which follow a certain set of "rules" based on the information that they know. This could be an issue with the fact that Pluribus has trained itself by playing itself instead of humans. While the results clearly show that Pluribus has found some kind of 'optimal' method to play, it would be interesting to see if it could actually maximize it's profits by learning the trends of its human opponents over time (learning on the fly with information gained each hand while it's playing).<br />
<br />
== Conclusion ==<br />
<br />
As Pluribus’s strategy was not developed with any human data and was trained by self-play only, it is an unbiased and different perspective on how optimal play can be attained.<br />
Developing a superhuman AI for multiplayer poker was a widely recognized<br />
milestone in this area and the major remaining milestone in computer poker.<br />
Pluribus’s success shows that despite the lack of known strong theoretical guarantees on performance in multiplayer games, there are large-scale, complex multiplayer imperfect information settings in which a carefully constructed self-play-with-search algorithm can produce superhuman strategies.<br />
<br />
== References ==<br />
<br />
Noam Brown and Tuomas Sandholm (July 11, 2019). Superhuman AI for multiplayer poker. Science 365.<br />
<br />
Osborne, Martin J.; Rubinstein, Ariel (12 Jul 1994). A Course in Game Theory. Cambridge, MA: MIT. p. 14.<br />
<br />
Justin Sermeno. (2020, November 17). Vanilla Counterfactual Regret Minimization for Engineers. https://justinsermeno.com/posts/cfr/#:~:text=Counterfactual%20regret%20minimization%20%28CFR%29%20is%20an%20algorithm%20that,decision.%20It%20can%20be%20positive%2C%20negative%2C%20or%20zero<br />
<br />
Brown, N., Bakhtin, A., Lerer, A., & Gong, Q. (2020). Combining deep reinforcement learning and search for imperfect-information games. Advances in Neural Information Processing Systems, 33.<br />
<br />
N. Brown and T. Sandholm, "Superhuman AI for heads-up no-limit poker: Libratus beats top professionals", Science, vol. 359, no. 6374, pp. 418-424, 2017. Available: 10.1126/science.aao1733 [Accessed 27 November 2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Superhuman_AI_for_Multiplayer_Poker&diff=47101Superhuman AI for Multiplayer Poker2020-11-27T23:37:29Z<p>Jcllau: /* References */</p>
<hr />
<div>== Presented by == <br />
Hansa Halim, Sanjana Rajendra Naik, Samka Marfua, Shawrupa Proshasty<br />
<br />
== Introduction ==<br />
<br />
A superintelligence is a hypothetical agent that possesses intelligence far surpassing that of the brightest and most gifted human minds. In the past two decades, most of the superhuman AI that was built can only beat human players in two-player zero-sum games. The most common strategy that the AI uses to beat those games is to find the most optimal Nash equilibrium. A Nash equilibrium is a pair of strategies such that either single-player switching to any ''other'' choice of strategy (while the other player's strategy remains unchanged) will result in a lower payout for the switching player. Intuitively this is similar to a locally optimal strategy for the players but is (i) not guaranteed to exist and (ii) may not be the truly optimal strategy (for example, in the "Prisoner's dilemma" the Nash equilibrium of both players betraying each other is not the optimal strategy).<br />
<br />
More specifically, in the game of poker, we only have AI models that can beat human players in two-player settings. An example of an AI model that can successfully beat two players in poker is Libratus, which is an AI developed in 2018 that also used MCCFR. Poker is a great challenge in AI and game theory because it captures the challenges in hidden information so elegantly. This means that developing a superhuman AI in multiplayer poker is the remaining great milestone in this field, because there is no polynomial-time algorithm that can find a Nash equilibrium in two-player non-zero-sum games, and having one would have surprising implications in computational complexity theory.<br />
<br />
In this paper, the AI which we call Pluribus is capable of defeating human professional poker players in Texas hold'em poker which is a six-player poker game and is the most commonly played format in the world. The algorithm that is used is not guaranteed to converge to a Nash algorithm outside of two-player zero-sum games. However, it uses a strong strategy that is capable of consistently defeating elite human professionals. This shows that despite not having strong theoretical guarantees on performance, they are capable of applying a wider class of superhuman strategies.<br />
<br />
== Nash Equilibrium in Multiplayer Games ==<br />
<br />
Many AI has reached superhuman performance in games like checkers, chess, two-player limit poker, Go, and two-player no-limit poker. Nash equilibrium has been proven to exist in all finite games and numerous infinite games. However, the challenge is to find the equilibrium. It is the best possible strategy and is unbeatable in two-player zero-sum games since it guarantees to not lose in expectation regardless of what the opponent is doing.<br />
<br />
To have a deeper understanding of Nash Equilibria we must first define some basic game theory concepts. The first one being a strategic game, in game theory a strategic game consists of a set of players, for each player a set of actions and for each player preferences (or payoffs) over the set of action profiles (set of combination of actions). With these three elements, we can model a wide variety of situations. Now a Nash Equilibrium is an action profile, with the property that no player can do better by changing their action, given that all other players' actions remain the same. A common illustration of Nash equilibria is the Prisoner's Dilemma. We also have mixed strategies and mixed strategy Nash equilibria. A mixed strategy is when instead of a player choosing an action they apply a probability distribution to their set of actions and pick randomly. Note that with mixed strategies we must look at the expected payoff of the player given the other players' strategies. Therefore a mixed strategy Nash Equilibria involves at least one player playing with a mixed strategy where no player can increase their expected payoff by changing their action, given that all other players' actions remain the same. Then we can define a pure Nash Equilibria to where no one is playing a mixed strategy. We also must be aware that a single game can have multiple pure Nash equilibria and mixed Nash equilibria. Also, Nash Equilibria are purely theoretical and depend on players acting optimally and being rational, this is not always the case with humans and we can act very irrationally. Therefore empirically we will see that games can have very unexpected outcomes and you may be able to get a better payoff if you move away from a strictly theoretical strategy and take advantage of your opponents irrational behavior. <br />
<br />
The insufficiency with current AI systems is that they only try to achieve Nash equilibriums instead of trying to actively detect and exploit weaknesses in opponents. At the Nash equilibrium, there is no incentive for any player to change their initial strategy, so it is a stable state of the system. For example, let's consider the game of Rock-Paper-Scissors, the Nash equilibrium is to randomly pick any option with equal probability. However, we can see that this means the best strategy that the opponent can have will result in a tie. Therefore, in this example, our player cannot win in expectation. Now let's try to combine the Nash equilibrium strategy and opponent exploitation. We can initially use the Nash equilibrium strategy and then change our strategy overtime to exploit the observed weaknesses of our opponent. For example, we switch to always play Rock against our opponent who always plays Scissors. However, by shifting away from the Nash equilibrium strategy, it opens up the possibility for our opponent to use our strategy against ourselves. For example, they notice we always play Rock and thus they will now always play Paper.<br />
<br />
Trying to approximate a Nash equilibrium is hard in theory, and in games with more than two players, it can only find a handful of possible strategies per player. Currently, existing techniques to find ways to exploit an opponent require way too many samples and are not competitive enough outside of small games. Finding a Nash equilibrium in three or more players is a great challenge. Even we can efficiently compute a Nash equilibrium in games with more than two players, it is still highly questionable if playing the Nash equilibrium strategy is a good choice. Additionally, if each player tries to find their own version of a Nash equilibrium, we could have infinitely many strategies and each player’s version of the equilibrium might not even be a Nash equilibrium.<br />
<br />
Consider the Lemonade Stand example from Figure 1 Below. We have 4 players and the goal for each player is to find a spot in the ring that is furthest away from every other player. This way, each lemonade stand can cover as much selling region as possible and generate maximum revenue. In the left circle, we have three different Nash equilibria distinguished by different colors which would benefit everyone. The right circle is an illustration of what would happen if each player decides to calculate their own Nash equilibrium.<br />
<br />
[[File:Lemonade_Example.png| 600px |center ]]<br />
<br />
<div align="center">Figure 1: Lemonade Stand Example</div><br />
<br />
From the right circle in Figure 1, we can see that when each player tries to calculate their own Nash equilibria, their own version of the equilibrium might not be a Nash equilibrium and thus they are not choosing the best possible location. This shows that attempting to find a Nash equilibrium is not the best strategy outside of two-player zero-sum games, and our goal should not be focused on finding a specific game-theoretic solution. Instead, we need to focus on observations and empirical results that consistently defeat human opponents.<br />
<br />
== Theoretical Analysis ==<br />
Pluribus uses forms of abstraction to make computations scalable. To simplify the complexity due to too many decision points, some actions are eliminated from consideration and similar decision points are grouped together and treated as identical. This process is called abstraction. Pluribus uses two kinds of abstraction: Action abstraction and information abstraction. Action abstraction reduces the number of different actions the AI needs to consider. For instance, it does not consider all bet sizes (exact number of bets it considers varies between 1 and 14 depending on the situation). Information abstraction groups together decision points that reveal similar information. For instance, the player’s cards and revealed board cards. This is only used to reason about situations on future betting rounds, never the current betting round.<br />
<br />
Pluribus uses a builtin strategy - “Blueprint strategy”, which it gradually improves by searching in real time in situations it finds itself in during the course of the game. In the first betting round pluribus uses the initial blueprint strategy when the number of decision points is small. The blueprint strategy is computed using Monte Carlo Counterfactual Regret Minimization (MCCFR) algorithm. CFR is commonly used in imperfect information games AI which is trained by repeatedly playing against copies of itself, without any data of human or prior AI play used as input. For ease of computation of CFR in this context, poker is represented <br />
as a game tree. A game tree is a tree structure where each node represents either a player’s decision, a chance event, or a terminal outcome and edges represent actions taken. <br />
<br />
[[File:Screen_Shot_2020-11-17_at_11.57.00_PM.png| 600px |center ]]<br />
<br />
<div align="center">Figure 1: Kuhn Poker (Simpler form of Poker) </div><br />
<br />
At the start of each iteration, MCCFR stimulates a hand of poker randomly (Cards held by a player at a given time) and designates one player as the traverser of the game tree. Once that is completed, the AI reviews the decision made by the traverser at a decision point in the game and investigates whether the decision was profitable. The AI compares its decision with other actions available to the traverser at that point and also with the future hypothetical decisions that would have been made following the other available actions. To evaluate a decision, the Counterfactual Regret factor is used. This is the difference between what the traverser would have expected to receive for choosing an action and actually received on the iteration. Thus regret is a numeric value, where a positive regret indicates you regret your decision, a negative regret indicates you are happy with your decision, and zero regret indicates that you are indifferent.<br />
<br />
The value of counterfactual regret for a decision is adjusted over the iterations as more scenarios or decision points are encountered. This means at the end of each iteration, the traverser’s strategy is updated so actions with higher counterfactual regret is chosen with higher probability. CFR minimizes regret over many iterations until the average strategy overall iterations converges and the average strategy is the approximated Nash equilibrium. CFR guarantees in all finite games that all counterfactual regrets grow sublinearly in the number of iterations. Pluribus uses Linear CFR in early iterations to reduce the influence of initial bad iterations i.e it assigns a weight of T to regret contributions at iteration T. This leads to the strategy improving more quickly in practice.<br />
<br />
An additional feature of Pluribus is that in the subgames, instead of assuming that all players play according to a single strategy, Pluribus considers that each player may choose between k different strategies specialized to each player when a decision point is reached. This results in the searcher choosing a more balanced strategy. For instance, if a player never bluffs while holding the best possible hand then the opponents would learn that fact and always fold in that scenario. To fold in that scenario is a balanced strategy than to bet.<br />
Therefore, the blueprint strategy is produced offline for the entire game and it is gradually improved while making real-time decisions during the game.<br />
<br />
== Experimental Results ==<br />
To test how well Pluribus functions, it was tested against human players in 2 formats. The first format included 5 human players and one copy of Pluribus (5H+1AI). The 13 human participants were poker players who have won more than $1M playing professionally and were provided with cash incentives to play their best. 10,000 hands of poker were played over 12 days with the 5H+1AI format by anonymizing the players by providing each of them with aliases that remained consistent throughout all their games. The aliases helped the players keep track of the tendencies and types of games played by each player over the 10,000 hands played. <br />
<br />
The second format included one human player and 5 copies of Pluribus (1H+5AI) . There were 2 more professional players who split another 10,000 hands of poker by playing 5000 hands each and followed the same aliasing process as the first format.<br />
Performance was measured using milli big blinds per game, mbb/game, (i.e. the initial amount of money the second player has to put in the pot) which is the standard measure in the AI field. Additionally, AIVAT was used as the variance reduction technique to control for luck in the games, and significance tests were run at a 95% significance level with one-tailed t-tests as a check for Pluribus’s performance in being profitable.<br />
<br />
Applying AIVAT the following were the results:<br />
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"<br />
! scope="col" | Format !! scope="col" | Average mbb/game !! scope="col" | Standard Error in mbb/game !! scope="col" | P-value of being profitable <br />
|-<br />
! scope="row" | 5H+1AI <br />
| 48 || 25 || 0.028 <br />
|-<br />
! scope="row" | 1H+5AI <br />
| 32 || 15 || 0.014<br />
|}<br />
[[File:top.PNG| 950px | x450px |left]]<br />
<br />
<br />
<div align="center">"Figure 3. Performance of Pluribus in the 5 humans + 1 AI experiment. The dots show Pluribus's performance at the end of each day of play. (Top) The lines show the win rate (solid line) plus or minus the standard error (dashed lines). (Bottom) The lines show the cumulative number of mbbs won (solid line) plus or minus the standard error (dashed lines). The relatively steady performance of Pluribus over the course of the 10,000-hand experiment also suggests that the humans were unable to find exploitable weaknesses in the bot."</div> <br />
<br />
Optimal play in Pluribus looks different from well-known poker conventions: A standard convention of “limping” in poker (calling the 'big blind' rather than folding or raising) is confirmed to be not optimal by Pluribus since it initially experimented with it but eliminated this from its strategy over its games of self-play. On the other hand, another convention of “donk betting” (starting a round by betting when someone else ended the previous round with a call) that is dismissed by players was adopted by Pluribus much more often than played by humans, and is proven to be profitable.<br />
<br />
== Discussion and Critiques ==<br />
<br />
Pluribus' Blueprint strategy and Abstraction methods effectively reduces the computational power required. Hence it was computed in 8 days and required less than 512 GB of memory, and costs about $144 to produce. This is in sharp contrast to all the other recent superhuman AI milestones for games. This is a great way the researchers have condensed down the problem to fit the current computational powers. <br />
<br />
Pluribus definitely shows that we can capture observational data and empirical results to construct a superhuman AI without requiring theoretical guarantees, this can be a baseline for future AI inventions and help in the research of AI. It would be interesting to use Pluribus's way of using non-theoretical approach in more real life problems such as autonomous driving or stock market trading.<br />
<br />
Extending this idea beyond two player zero sum games will have many applications in real life.<br />
<br />
The summary for Superhuman AI for Multiplayer Poker is very well written, with a detailed explanation of the concept, steps, and result and with a combination of visual images. However, it seems that the experiment of the study is not well designed. For example: sample selection is not strict and well defined, this could cause selection bias introduced into the result and thus making it not generalizable.<br />
<br />
Superhuman AI, while sounding superior, is actually not uncommon. There has been many endeavours on mastering poker such as the Recursive Belief-based Learning (ReBeL) by Facebook Research. They pursued a method of reinforcement learning on partially observable Markov decision process which was inspired by the recent successes of AlphaZero. For Pluribus to demonstrate how effective it is compared to the state-of-the-art, it should run some experiments against ReBeL.<br />
<br />
This is a very interesting topic, and this summary is clear enough for readers to understand. I think this application not only can apply in poker, maybe thinking more applications in other area? There are many famous AI that really changing our life. For example, AlphaGo and AlphaStar, which are developed by Google DeepMind, defeated professional gamers. Discussing more this will be interesting.<br />
<br />
One of the biggest issues when applying AI to games against humans (when not all information is known, ie, opponents cards) is the assumption is generally made that the human players are rational players which follow a certain set of "rules" based on the information that they know. This could be an issue with the fact that Pluribus has trained itself by playing itself instead of humans. While the results clearly show that Pluribus has found some kind of 'optimal' method to play, it would be interesting to see if it could actually maximize it's profits by learning the trends of its human opponents over time (learning on the fly with information gained each hand while it's playing).<br />
<br />
== Conclusion ==<br />
<br />
As Pluribus’s strategy was not developed with any human data and was trained by self-play only, it is an unbiased and different perspective on how optimal play can be attained.<br />
Developing a superhuman AI for multiplayer poker was a widely recognized<br />
milestone in this area and the major remaining milestone in computer poker.<br />
Pluribus’s success shows that despite the lack of known strong theoretical guarantees on performance in multiplayer games, there are large-scale, complex multiplayer imperfect information settings in which a carefully constructed self-play-with-search algorithm can produce superhuman strategies.<br />
<br />
== References ==<br />
<br />
Noam Brown and Tuomas Sandholm (July 11, 2019). Superhuman AI for multiplayer poker. Science 365.<br />
<br />
Osborne, Martin J.; Rubinstein, Ariel (12 Jul 1994). A Course in Game Theory. Cambridge, MA: MIT. p. 14.<br />
<br />
Justin Sermeno. (2020, November 17). Vanilla Counterfactual Regret Minimization for Engineers. https://justinsermeno.com/posts/cfr/#:~:text=Counterfactual%20regret%20minimization%20%28CFR%29%20is%20an%20algorithm%20that,decision.%20It%20can%20be%20positive%2C%20negative%2C%20or%20zero<br />
<br />
Brown, N., Bakhtin, A., Lerer, A., & Gong, Q. (2020). Combining deep reinforcement learning and search for imperfect-information games. Advances in Neural Information Processing Systems, 33.<br />
<br />
N. Brown and T. Sandholm, "Superhuman AI for heads-up no-limit poker: Libratus beats top professionals", Science, vol. 359, no. 6374, pp. 418-424, 2017. Available: 10.1126/science.aao1733 [Accessed 27 November 2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Superhuman_AI_for_Multiplayer_Poker&diff=47100Superhuman AI for Multiplayer Poker2020-11-27T23:35:05Z<p>Jcllau: /* Introduction */</p>
<hr />
<div>== Presented by == <br />
Hansa Halim, Sanjana Rajendra Naik, Samka Marfua, Shawrupa Proshasty<br />
<br />
== Introduction ==<br />
<br />
A superintelligence is a hypothetical agent that possesses intelligence far surpassing that of the brightest and most gifted human minds. In the past two decades, most of the superhuman AI that was built can only beat human players in two-player zero-sum games. The most common strategy that the AI uses to beat those games is to find the most optimal Nash equilibrium. A Nash equilibrium is a pair of strategies such that either single-player switching to any ''other'' choice of strategy (while the other player's strategy remains unchanged) will result in a lower payout for the switching player. Intuitively this is similar to a locally optimal strategy for the players but is (i) not guaranteed to exist and (ii) may not be the truly optimal strategy (for example, in the "Prisoner's dilemma" the Nash equilibrium of both players betraying each other is not the optimal strategy).<br />
<br />
More specifically, in the game of poker, we only have AI models that can beat human players in two-player settings. An example of an AI model that can successfully beat two players in poker is Libratus, which is an AI developed in 2018 that also used MCCFR. Poker is a great challenge in AI and game theory because it captures the challenges in hidden information so elegantly. This means that developing a superhuman AI in multiplayer poker is the remaining great milestone in this field, because there is no polynomial-time algorithm that can find a Nash equilibrium in two-player non-zero-sum games, and having one would have surprising implications in computational complexity theory.<br />
<br />
In this paper, the AI which we call Pluribus is capable of defeating human professional poker players in Texas hold'em poker which is a six-player poker game and is the most commonly played format in the world. The algorithm that is used is not guaranteed to converge to a Nash algorithm outside of two-player zero-sum games. However, it uses a strong strategy that is capable of consistently defeating elite human professionals. This shows that despite not having strong theoretical guarantees on performance, they are capable of applying a wider class of superhuman strategies.<br />
<br />
== Nash Equilibrium in Multiplayer Games ==<br />
<br />
Many AI has reached superhuman performance in games like checkers, chess, two-player limit poker, Go, and two-player no-limit poker. Nash equilibrium has been proven to exist in all finite games and numerous infinite games. However, the challenge is to find the equilibrium. It is the best possible strategy and is unbeatable in two-player zero-sum games since it guarantees to not lose in expectation regardless of what the opponent is doing.<br />
<br />
To have a deeper understanding of Nash Equilibria we must first define some basic game theory concepts. The first one being a strategic game, in game theory a strategic game consists of a set of players, for each player a set of actions and for each player preferences (or payoffs) over the set of action profiles (set of combination of actions). With these three elements, we can model a wide variety of situations. Now a Nash Equilibrium is an action profile, with the property that no player can do better by changing their action, given that all other players' actions remain the same. A common illustration of Nash equilibria is the Prisoner's Dilemma. We also have mixed strategies and mixed strategy Nash equilibria. A mixed strategy is when instead of a player choosing an action they apply a probability distribution to their set of actions and pick randomly. Note that with mixed strategies we must look at the expected payoff of the player given the other players' strategies. Therefore a mixed strategy Nash Equilibria involves at least one player playing with a mixed strategy where no player can increase their expected payoff by changing their action, given that all other players' actions remain the same. Then we can define a pure Nash Equilibria to where no one is playing a mixed strategy. We also must be aware that a single game can have multiple pure Nash equilibria and mixed Nash equilibria. Also, Nash Equilibria are purely theoretical and depend on players acting optimally and being rational, this is not always the case with humans and we can act very irrationally. Therefore empirically we will see that games can have very unexpected outcomes and you may be able to get a better payoff if you move away from a strictly theoretical strategy and take advantage of your opponents irrational behavior. <br />
<br />
The insufficiency with current AI systems is that they only try to achieve Nash equilibriums instead of trying to actively detect and exploit weaknesses in opponents. At the Nash equilibrium, there is no incentive for any player to change their initial strategy, so it is a stable state of the system. For example, let's consider the game of Rock-Paper-Scissors, the Nash equilibrium is to randomly pick any option with equal probability. However, we can see that this means the best strategy that the opponent can have will result in a tie. Therefore, in this example, our player cannot win in expectation. Now let's try to combine the Nash equilibrium strategy and opponent exploitation. We can initially use the Nash equilibrium strategy and then change our strategy overtime to exploit the observed weaknesses of our opponent. For example, we switch to always play Rock against our opponent who always plays Scissors. However, by shifting away from the Nash equilibrium strategy, it opens up the possibility for our opponent to use our strategy against ourselves. For example, they notice we always play Rock and thus they will now always play Paper.<br />
<br />
Trying to approximate a Nash equilibrium is hard in theory, and in games with more than two players, it can only find a handful of possible strategies per player. Currently, existing techniques to find ways to exploit an opponent require way too many samples and are not competitive enough outside of small games. Finding a Nash equilibrium in three or more players is a great challenge. Even we can efficiently compute a Nash equilibrium in games with more than two players, it is still highly questionable if playing the Nash equilibrium strategy is a good choice. Additionally, if each player tries to find their own version of a Nash equilibrium, we could have infinitely many strategies and each player’s version of the equilibrium might not even be a Nash equilibrium.<br />
<br />
Consider the Lemonade Stand example from Figure 1 Below. We have 4 players and the goal for each player is to find a spot in the ring that is furthest away from every other player. This way, each lemonade stand can cover as much selling region as possible and generate maximum revenue. In the left circle, we have three different Nash equilibria distinguished by different colors which would benefit everyone. The right circle is an illustration of what would happen if each player decides to calculate their own Nash equilibrium.<br />
<br />
[[File:Lemonade_Example.png| 600px |center ]]<br />
<br />
<div align="center">Figure 1: Lemonade Stand Example</div><br />
<br />
From the right circle in Figure 1, we can see that when each player tries to calculate their own Nash equilibria, their own version of the equilibrium might not be a Nash equilibrium and thus they are not choosing the best possible location. This shows that attempting to find a Nash equilibrium is not the best strategy outside of two-player zero-sum games, and our goal should not be focused on finding a specific game-theoretic solution. Instead, we need to focus on observations and empirical results that consistently defeat human opponents.<br />
<br />
== Theoretical Analysis ==<br />
Pluribus uses forms of abstraction to make computations scalable. To simplify the complexity due to too many decision points, some actions are eliminated from consideration and similar decision points are grouped together and treated as identical. This process is called abstraction. Pluribus uses two kinds of abstraction: Action abstraction and information abstraction. Action abstraction reduces the number of different actions the AI needs to consider. For instance, it does not consider all bet sizes (exact number of bets it considers varies between 1 and 14 depending on the situation). Information abstraction groups together decision points that reveal similar information. For instance, the player’s cards and revealed board cards. This is only used to reason about situations on future betting rounds, never the current betting round.<br />
<br />
Pluribus uses a builtin strategy - “Blueprint strategy”, which it gradually improves by searching in real time in situations it finds itself in during the course of the game. In the first betting round pluribus uses the initial blueprint strategy when the number of decision points is small. The blueprint strategy is computed using Monte Carlo Counterfactual Regret Minimization (MCCFR) algorithm. CFR is commonly used in imperfect information games AI which is trained by repeatedly playing against copies of itself, without any data of human or prior AI play used as input. For ease of computation of CFR in this context, poker is represented <br />
as a game tree. A game tree is a tree structure where each node represents either a player’s decision, a chance event, or a terminal outcome and edges represent actions taken. <br />
<br />
[[File:Screen_Shot_2020-11-17_at_11.57.00_PM.png| 600px |center ]]<br />
<br />
<div align="center">Figure 1: Kuhn Poker (Simpler form of Poker) </div><br />
<br />
At the start of each iteration, MCCFR stimulates a hand of poker randomly (Cards held by a player at a given time) and designates one player as the traverser of the game tree. Once that is completed, the AI reviews the decision made by the traverser at a decision point in the game and investigates whether the decision was profitable. The AI compares its decision with other actions available to the traverser at that point and also with the future hypothetical decisions that would have been made following the other available actions. To evaluate a decision, the Counterfactual Regret factor is used. This is the difference between what the traverser would have expected to receive for choosing an action and actually received on the iteration. Thus regret is a numeric value, where a positive regret indicates you regret your decision, a negative regret indicates you are happy with your decision, and zero regret indicates that you are indifferent.<br />
<br />
The value of counterfactual regret for a decision is adjusted over the iterations as more scenarios or decision points are encountered. This means at the end of each iteration, the traverser’s strategy is updated so actions with higher counterfactual regret is chosen with higher probability. CFR minimizes regret over many iterations until the average strategy overall iterations converges and the average strategy is the approximated Nash equilibrium. CFR guarantees in all finite games that all counterfactual regrets grow sublinearly in the number of iterations. Pluribus uses Linear CFR in early iterations to reduce the influence of initial bad iterations i.e it assigns a weight of T to regret contributions at iteration T. This leads to the strategy improving more quickly in practice.<br />
<br />
An additional feature of Pluribus is that in the subgames, instead of assuming that all players play according to a single strategy, Pluribus considers that each player may choose between k different strategies specialized to each player when a decision point is reached. This results in the searcher choosing a more balanced strategy. For instance, if a player never bluffs while holding the best possible hand then the opponents would learn that fact and always fold in that scenario. To fold in that scenario is a balanced strategy than to bet.<br />
Therefore, the blueprint strategy is produced offline for the entire game and it is gradually improved while making real-time decisions during the game.<br />
<br />
== Experimental Results ==<br />
To test how well Pluribus functions, it was tested against human players in 2 formats. The first format included 5 human players and one copy of Pluribus (5H+1AI). The 13 human participants were poker players who have won more than $1M playing professionally and were provided with cash incentives to play their best. 10,000 hands of poker were played over 12 days with the 5H+1AI format by anonymizing the players by providing each of them with aliases that remained consistent throughout all their games. The aliases helped the players keep track of the tendencies and types of games played by each player over the 10,000 hands played. <br />
<br />
The second format included one human player and 5 copies of Pluribus (1H+5AI) . There were 2 more professional players who split another 10,000 hands of poker by playing 5000 hands each and followed the same aliasing process as the first format.<br />
Performance was measured using milli big blinds per game, mbb/game, (i.e. the initial amount of money the second player has to put in the pot) which is the standard measure in the AI field. Additionally, AIVAT was used as the variance reduction technique to control for luck in the games, and significance tests were run at a 95% significance level with one-tailed t-tests as a check for Pluribus’s performance in being profitable.<br />
<br />
Applying AIVAT the following were the results:<br />
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"<br />
! scope="col" | Format !! scope="col" | Average mbb/game !! scope="col" | Standard Error in mbb/game !! scope="col" | P-value of being profitable <br />
|-<br />
! scope="row" | 5H+1AI <br />
| 48 || 25 || 0.028 <br />
|-<br />
! scope="row" | 1H+5AI <br />
| 32 || 15 || 0.014<br />
|}<br />
[[File:top.PNG| 950px | x450px |left]]<br />
<br />
<br />
<div align="center">"Figure 3. Performance of Pluribus in the 5 humans + 1 AI experiment. The dots show Pluribus's performance at the end of each day of play. (Top) The lines show the win rate (solid line) plus or minus the standard error (dashed lines). (Bottom) The lines show the cumulative number of mbbs won (solid line) plus or minus the standard error (dashed lines). The relatively steady performance of Pluribus over the course of the 10,000-hand experiment also suggests that the humans were unable to find exploitable weaknesses in the bot."</div> <br />
<br />
Optimal play in Pluribus looks different from well-known poker conventions: A standard convention of “limping” in poker (calling the 'big blind' rather than folding or raising) is confirmed to be not optimal by Pluribus since it initially experimented with it but eliminated this from its strategy over its games of self-play. On the other hand, another convention of “donk betting” (starting a round by betting when someone else ended the previous round with a call) that is dismissed by players was adopted by Pluribus much more often than played by humans, and is proven to be profitable.<br />
<br />
== Discussion and Critiques ==<br />
<br />
Pluribus' Blueprint strategy and Abstraction methods effectively reduces the computational power required. Hence it was computed in 8 days and required less than 512 GB of memory, and costs about $144 to produce. This is in sharp contrast to all the other recent superhuman AI milestones for games. This is a great way the researchers have condensed down the problem to fit the current computational powers. <br />
<br />
Pluribus definitely shows that we can capture observational data and empirical results to construct a superhuman AI without requiring theoretical guarantees, this can be a baseline for future AI inventions and help in the research of AI. It would be interesting to use Pluribus's way of using non-theoretical approach in more real life problems such as autonomous driving or stock market trading.<br />
<br />
Extending this idea beyond two player zero sum games will have many applications in real life.<br />
<br />
The summary for Superhuman AI for Multiplayer Poker is very well written, with a detailed explanation of the concept, steps, and result and with a combination of visual images. However, it seems that the experiment of the study is not well designed. For example: sample selection is not strict and well defined, this could cause selection bias introduced into the result and thus making it not generalizable.<br />
<br />
Superhuman AI, while sounding superior, is actually not uncommon. There has been many endeavours on mastering poker such as the Recursive Belief-based Learning (ReBeL) by Facebook Research. They pursued a method of reinforcement learning on partially observable Markov decision process which was inspired by the recent successes of AlphaZero. For Pluribus to demonstrate how effective it is compared to the state-of-the-art, it should run some experiments against ReBeL.<br />
<br />
This is a very interesting topic, and this summary is clear enough for readers to understand. I think this application not only can apply in poker, maybe thinking more applications in other area? There are many famous AI that really changing our life. For example, AlphaGo and AlphaStar, which are developed by Google DeepMind, defeated professional gamers. Discussing more this will be interesting.<br />
<br />
One of the biggest issues when applying AI to games against humans (when not all information is known, ie, opponents cards) is the assumption is generally made that the human players are rational players which follow a certain set of "rules" based on the information that they know. This could be an issue with the fact that Pluribus has trained itself by playing itself instead of humans. While the results clearly show that Pluribus has found some kind of 'optimal' method to play, it would be interesting to see if it could actually maximize it's profits by learning the trends of its human opponents over time (learning on the fly with information gained each hand while it's playing).<br />
<br />
== Conclusion ==<br />
<br />
As Pluribus’s strategy was not developed with any human data and was trained by self-play only, it is an unbiased and different perspective on how optimal play can be attained.<br />
Developing a superhuman AI for multiplayer poker was a widely recognized<br />
milestone in this area and the major remaining milestone in computer poker.<br />
Pluribus’s success shows that despite the lack of known strong theoretical guarantees on performance in multiplayer games, there are large-scale, complex multiplayer imperfect information settings in which a carefully constructed self-play-with-search algorithm can produce superhuman strategies.<br />
<br />
== References ==<br />
<br />
Noam Brown and Tuomas Sandholm (July 11, 2019). Superhuman AI for multiplayer poker. Science 365.<br />
<br />
Osborne, Martin J.; Rubinstein, Ariel (12 Jul 1994). A Course in Game Theory. Cambridge, MA: MIT. p. 14.<br />
<br />
Justin Sermeno. (2020, November 17). Vanilla Counterfactual Regret Minimization for Engineers. https://justinsermeno.com/posts/cfr/#:~:text=Counterfactual%20regret%20minimization%20%28CFR%29%20is%20an%20algorithm%20that,decision.%20It%20can%20be%20positive%2C%20negative%2C%20or%20zero<br />
<br />
Brown, N., Bakhtin, A., Lerer, A., & Gong, Q. (2020). Combining deep reinforcement learning and search for imperfect-information games. Advances in Neural Information Processing Systems, 33.</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:G25_Figure2_right.png&diff=46859File:G25 Figure2 right.png2020-11-26T22:10:37Z<p>Jcllau: </p>
<hr />
<div></div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:G25_Figure2_left.png&diff=46858File:G25 Figure2 left.png2020-11-26T22:10:20Z<p>Jcllau: </p>
<hr />
<div></div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46857Loss Function Search for Face Recognition2020-11-26T22:09:57Z<p>Jcllau: /* Results on MegaFace and Trillion-Pairs */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and <math>s</math> represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. It is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
<center>[[Image:G25_Figure1.png|300px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]</center><br />
<center>Figure 1: Reinforcement Learning scenario [4]</center><br />
<br />
The reward function is what guides the agent to move into a certain direction. As mentioned above, the system receives feedback from the data to achieve the best outcome. This is caused by the reward being edited based on the feedback it receives when a task is completed [5]. <br />
<br />
In this paper, RL is being used to generate a distribution of the hyperparameter <math>\mu</math> for the SoftMax equation using the reward function. <math>\mu</math> updates after each epoch from the reward function. <br />
<br />
<center><math>\mu_{e+1}=\mu_e + \eta \frac{1}{B} \sum_{i=1}^B R{(a_i)}{\nabla_a}log{(g(a_i;\mu,\sigma))}</math></center><br />
<br />
=== Optimization ===<br />
Calculating the reward involves a standard bi-level optimization problem, which involves a hyperparameter ({<math>a_1,a_2,…,a_B</math>}) that can be used for minimizing one objective function while maximizing another objective function simultaneously:<br />
<br />
<center><math>max_a R(a)=r(M_{w^*(a)},S_v)</math></center><br />
<center><math>w^*(a)=_w \sum_{(x,y) \in S_t} L^a (M_w(x),y)</math></center><br />
<br />
In this case, the loss function takes the training set <math>S_t</math> and the reward function takes the validation set <math>S_v</math>. The weights <math>w</math> are trained such that the loss function is minimized while the reward function is maximized. The calculated reward for each model ({<math>M_{we1},M_{we2},…,M_{weB}</math>}) yields the corresponding score, then the algorithm chooses the one with the highest score for model index selection. With the model containing the highest score being used in the next epoch, this process is repeated until the training reaches convergence. At the end, the algorithm takes the model with the highest score without retraining.<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
For LFW, there is not a noticeable difference between the algorithms proposed in this paper and the other algorithms. However, AM-Softmax achieved higher results than Search-Softmax. Random-Softmax achieved the highest results by 0.03%.<br />
<br />
Random-Softmax outperforms baseline Soft-max and is comparable to most of the margin-based softmax. Search-Softmax boost the performance and better most methods specifically when training CASIA-WebFace-R data set, it achieves 0.72% average improvement over AM-Softmax. The reason the model proposed by the paper gives better results is because of their optimization strategy which helps boost the discimination power. Also the sampled candidate from the paper’s proposed search space can well approximate the margin-based loss functions. More tests need to happen to more complicated protocols to test the performance further. Not a lot of improvement has been shown on those test sets, since they are relatively simple and the performance of all the methods on these test sets are near saturation. <br />
<br />
<center>Table 1.Verification performance (%) of different methods on the test sets LFW, SLLFW, CALFW, CPLFW, AgeDB and CFP. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<br />
<center>[[Image:G25_Table1.png|900px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on RFW ===<br />
The RFW dataset measures racial bias which consists of Caucasian, Indian, Asian, and African. Using this as the test set, Random-softmax and Search-softmax performed better than the other methods. Random-softmax outperforms the baseline softmax by a large margin which means reducing the softmax probability will enhance the feature discrimination for face recognition. It is also observed that the reward guided search-softmax method is more likely to enhance the discriminative feature learning resulting in higher performance as shown in Table 2 and Table 3. <br />
<br />
<center>Table 2. Verification performance (%) of different methods on the test set RFW. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table2.png|500px |alt=Alt text|Title text]]</center><br />
<br />
<br />
<center>Table 3. Verification performance (%) of different methods on the test set RFW. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table3.png|500px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
The different loss functions are tested again with more complicated protocols. The identification (Id.) Rank-1 and the verification (Veri.) with the true positive rate (TPR) at low false acceptance rate (FAR) at <math>1e-3</math> on MegaFace, the identification TPR@FAR = <math>1e-6</math> and the verification TPR@FAR = <math>1e-9</math> on Trillion-Pairs are reported on Table 4 and 5.<br />
<br />
On the test sets MegaFace and Trillion-Pairs, Search-softmax achieves the best performance over all other alternative methods. On MegaFace, Search-softmax beat the best competitor AM-softmax by a large margin. It also outperformed AM-LFS due to new designed search space. <br />
<br />
<center>Table 4. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table4.png|450px |alt=Alt text|Title text]]</center><br />
<br />
<br />
<center>Table 5. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table5.png|450px |alt=Alt text|Title text]]</center><br />
<br />
From the CMC curves and ROC curves in Figure 2, similar trends are observed at other measures. There is a same trend on Trillion-Pairs where Search-softmax loss is found to be superior with 4% improvements with CASIA-WebFace-R and 1% improvements with MS-Celeb-1M-v1c-R at both the identification and verification. Based on these experiments, Search-Softmax loss can perform well, especially with a low false positive rate and it shows a strong generalization ability for face recognition.<br />
<br />
<center>[[Image:G25_Figure2_left.png|450px |alt=Alt text|Title text]] [[Image:G25_Figure2_right.png|450px |alt=Alt text|Title text]]</center><br />
<center>Figure 2. From Left to Right: CMC curves and ROC curves on MegaFace Set with training set CASIA-WebFace-R, CMC curves and ROC curves on MegaFace Set with training set MS-Celeb-1M-v1c-R [1].</center><br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
== Critiques ==<br />
* Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
* Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
* AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
* The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46856Loss Function Search for Face Recognition2020-11-26T22:07:32Z<p>Jcllau: /* Optimization */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and <math>s</math> represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. It is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
<center>[[Image:G25_Figure1.png|300px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]</center><br />
<center>Figure 1: Reinforcement Learning scenario [4]</center><br />
<br />
The reward function is what guides the agent to move into a certain direction. As mentioned above, the system receives feedback from the data to achieve the best outcome. This is caused by the reward being edited based on the feedback it receives when a task is completed [5]. <br />
<br />
In this paper, RL is being used to generate a distribution of the hyperparameter <math>\mu</math> for the SoftMax equation using the reward function. <math>\mu</math> updates after each epoch from the reward function. <br />
<br />
<center><math>\mu_{e+1}=\mu_e + \eta \frac{1}{B} \sum_{i=1}^B R{(a_i)}{\nabla_a}log{(g(a_i;\mu,\sigma))}</math></center><br />
<br />
=== Optimization ===<br />
Calculating the reward involves a standard bi-level optimization problem, which involves a hyperparameter ({<math>a_1,a_2,…,a_B</math>}) that can be used for minimizing one objective function while maximizing another objective function simultaneously:<br />
<br />
<center><math>max_a R(a)=r(M_{w^*(a)},S_v)</math></center><br />
<center><math>w^*(a)=_w \sum_{(x,y) \in S_t} L^a (M_w(x),y)</math></center><br />
<br />
In this case, the loss function takes the training set <math>S_t</math> and the reward function takes the validation set <math>S_v</math>. The weights <math>w</math> are trained such that the loss function is minimized while the reward function is maximized. The calculated reward for each model ({<math>M_{we1},M_{we2},…,M_{weB}</math>}) yields the corresponding score, then the algorithm chooses the one with the highest score for model index selection. With the model containing the highest score being used in the next epoch, this process is repeated until the training reaches convergence. At the end, the algorithm takes the model with the highest score without retraining.<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
For LFW, there is not a noticeable difference between the algorithms proposed in this paper and the other algorithms. However, AM-Softmax achieved higher results than Search-Softmax. Random-Softmax achieved the highest results by 0.03%.<br />
<br />
Random-Softmax outperforms baseline Soft-max and is comparable to most of the margin-based softmax. Search-Softmax boost the performance and better most methods specifically when training CASIA-WebFace-R data set, it achieves 0.72% average improvement over AM-Softmax. The reason the model proposed by the paper gives better results is because of their optimization strategy which helps boost the discimination power. Also the sampled candidate from the paper’s proposed search space can well approximate the margin-based loss functions. More tests need to happen to more complicated protocols to test the performance further. Not a lot of improvement has been shown on those test sets, since they are relatively simple and the performance of all the methods on these test sets are near saturation. <br />
<br />
<center>Table 1.Verification performance (%) of different methods on the test sets LFW, SLLFW, CALFW, CPLFW, AgeDB and CFP. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<br />
<center>[[Image:G25_Table1.png|900px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on RFW ===<br />
The RFW dataset measures racial bias which consists of Caucasian, Indian, Asian, and African. Using this as the test set, Random-softmax and Search-softmax performed better than the other methods. Random-softmax outperforms the baseline softmax by a large margin which means reducing the softmax probability will enhance the feature discrimination for face recognition. It is also observed that the reward guided search-softmax method is more likely to enhance the discriminative feature learning resulting in higher performance as shown in Table 2 and Table 3. <br />
<br />
<center>Table 2. Verification performance (%) of different methods on the test set RFW. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table2.png|500px |alt=Alt text|Title text]]</center><br />
<br />
<br />
<center>Table 3. Verification performance (%) of different methods on the test set RFW. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table3.png|500px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
The different loss functions are tested again with more complicated protocols. The identification (Id.) Rank-1 and the verification (Veri.) with the true positive rate (TPR) at low false acceptance rate (FAR) at <math>1e-3</math> on MegaFace, the identification TPR@FAR = <math>1e-6</math> and the verification TPR@FAR = <math>1e-9</math> on Trillion-Pairs are reported on Table 4 and 5.<br />
<br />
On the test sets MegaFace and Trillion-Pairs, Search-softmax achieves the best performance over all other alternative methods. On MegaFace, Search-softmax beat the best competitor AM-softmax by a large margin. It also outperformed AM-LFS due to new designed search space. <br />
<br />
<center>Table 4. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table4.png|450px |alt=Alt text|Title text]]</center><br />
<br />
<br />
<center>Table 5. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table5.png|450px |alt=Alt text|Title text]]</center><br />
<br />
From the CMC curves and ROC curves in Figure 2, similar trends are observed at other measures. There is a same trend on Trillion-Pairs where Search-softmax loss is found to be superior with 4% improvements with CASIA-WebFace-R and 1% improvements with MS-Celeb-1M-v1c-R at both the identification and verification. Based on these experiments, Search-Softmax loss can perform well, especially with a low false positive rate and it shows a strong generalization ability for face recognition.<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
== Critiques ==<br />
* Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
* Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
* AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
* The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46855Loss Function Search for Face Recognition2020-11-26T22:05:45Z<p>Jcllau: /* Reward-Guided Search */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and <math>s</math> represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. It is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
<center>[[Image:G25_Figure1.png|300px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]</center><br />
<center>Figure 1: Reinforcement Learning scenario [4]</center><br />
<br />
The reward function is what guides the agent to move into a certain direction. As mentioned above, the system receives feedback from the data to achieve the best outcome. This is caused by the reward being edited based on the feedback it receives when a task is completed [5]. <br />
<br />
In this paper, RL is being used to generate a distribution of the hyperparameter <math>\mu</math> for the SoftMax equation using the reward function. <math>\mu</math> updates after each epoch from the reward function. <br />
<br />
<center><math>\mu_{e+1}=\mu_e + \eta \frac{1}{B} \sum_{i=1}^B R{(a_i)}{\nabla_a}log{(g(a_i;\mu,\sigma))}</math></center><br />
<br />
=== Optimization ===<br />
Calculating the reward involves a standard bi-level optimization problem, which involves a hyperparameter ({<math>a_1,a_2,…,a_B</math>}) that can be used for minimizing one objective function while maximizing another objective function simultaneously:<br />
<br />
<center><math>max_a R(a)=r(M_{w^*(a)},S_v)</math></center><br />
<center><math>w^*(a)=_w \sum_{(x,y) \in S_t} L^a (M_w(x),y)</math></center><br />
<br />
In this case, the loss function takes the training set St and the reward function takes the validation set <math>S_v</math>. The weights <math>w</math> are trained such that the loss function is minimized while the reward function is maximized. The calculated reward for each model ({<math>M_{we1},M_{we2},…,M_{weB}</math>}) yields the corresponding score, then the algorithm chooses the one with the highest score for model index selection. With the model containing the highest score being used in the next epoch, this process is repeated until the training reaches convergence. At the end, the algorithm takes the model with the highest score without retraining.<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
For LFW, there is not a noticeable difference between the algorithms proposed in this paper and the other algorithms. However, AM-Softmax achieved higher results than Search-Softmax. Random-Softmax achieved the highest results by 0.03%.<br />
<br />
Random-Softmax outperforms baseline Soft-max and is comparable to most of the margin-based softmax. Search-Softmax boost the performance and better most methods specifically when training CASIA-WebFace-R data set, it achieves 0.72% average improvement over AM-Softmax. The reason the model proposed by the paper gives better results is because of their optimization strategy which helps boost the discimination power. Also the sampled candidate from the paper’s proposed search space can well approximate the margin-based loss functions. More tests need to happen to more complicated protocols to test the performance further. Not a lot of improvement has been shown on those test sets, since they are relatively simple and the performance of all the methods on these test sets are near saturation. <br />
<br />
<center>Table 1.Verification performance (%) of different methods on the test sets LFW, SLLFW, CALFW, CPLFW, AgeDB and CFP. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<br />
<center>[[Image:G25_Table1.png|900px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on RFW ===<br />
The RFW dataset measures racial bias which consists of Caucasian, Indian, Asian, and African. Using this as the test set, Random-softmax and Search-softmax performed better than the other methods. Random-softmax outperforms the baseline softmax by a large margin which means reducing the softmax probability will enhance the feature discrimination for face recognition. It is also observed that the reward guided search-softmax method is more likely to enhance the discriminative feature learning resulting in higher performance as shown in Table 2 and Table 3. <br />
<br />
<center>Table 2. Verification performance (%) of different methods on the test set RFW. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table2.png|500px |alt=Alt text|Title text]]</center><br />
<br />
<br />
<center>Table 3. Verification performance (%) of different methods on the test set RFW. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table3.png|500px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
The different loss functions are tested again with more complicated protocols. The identification (Id.) Rank-1 and the verification (Veri.) with the true positive rate (TPR) at low false acceptance rate (FAR) at <math>1e-3</math> on MegaFace, the identification TPR@FAR = <math>1e-6</math> and the verification TPR@FAR = <math>1e-9</math> on Trillion-Pairs are reported on Table 4 and 5.<br />
<br />
On the test sets MegaFace and Trillion-Pairs, Search-softmax achieves the best performance over all other alternative methods. On MegaFace, Search-softmax beat the best competitor AM-softmax by a large margin. It also outperformed AM-LFS due to new designed search space. <br />
<br />
<center>Table 4. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table4.png|450px |alt=Alt text|Title text]]</center><br />
<br />
<br />
<center>Table 5. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table5.png|450px |alt=Alt text|Title text]]</center><br />
<br />
From the CMC curves and ROC curves in Figure 2, similar trends are observed at other measures. There is a same trend on Trillion-Pairs where Search-softmax loss is found to be superior with 4% improvements with CASIA-WebFace-R and 1% improvements with MS-Celeb-1M-v1c-R at both the identification and verification. Based on these experiments, Search-Softmax loss can perform well, especially with a low false positive rate and it shows a strong generalization ability for face recognition.<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
== Critiques ==<br />
* Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
* Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
* AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
* The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46852Loss Function Search for Face Recognition2020-11-26T21:55:09Z<p>Jcllau: </p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and <math>s</math> represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
<center>[[Image:G25_Figure1.png|300px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]</center><br />
<center>Figure 1: Reinforcement Learning scenario [4]</center><br />
<br />
The reward function is what guides the agent to move into a certain direction. As mentioned above, the system receives feedback from the data to achieve the best outcome. This is caused by the reward being edited based on the feedback it receives when a task is completed [5]. <br />
<br />
In this paper, RL is being used to generate a distribution of the hyperparameter <math>\mu</math> for the SoftMax equation using the reward function. <math>\mu</math> updates after each epoch from the reward function. <br />
<br />
<center><math>\mu_{e+1}=\mu_e + \eta \frac{1}{B} \sum_{i=1}^B R{(a_i)}{\nabla_a}log{(g(a_i;\mu,\sigma))}</math></center><br />
<br />
=== Optimization ===<br />
Calculating the reward involves a standard bi-level optimization problem, which involves a hyperparameter ({<math>a_1,a_2,…,a_B</math>}) that can be used for minimizing one objective function while maximizing another objective function simultaneously:<br />
<br />
<center><math>max_a R(a)=r(M_{w^*(a)},S_v)</math></center><br />
<center><math>w^*(a)=_w \sum_{(x,y) \in S_t} L^a (M_w(x),y)</math></center><br />
<br />
In this case, the loss function takes the training set St and the reward function takes the validation set <math>S_v</math>. The weights <math>w</math> are trained such that the loss function is minimized while the reward function is maximized. The calculated reward for each model ({<math>M_{we1},M_{we2},…,M_{weB}</math>}) yields the corresponding score, then the algorithm chooses the one with the highest score for model index selection. With the model containing the highest score being used in the next epoch, this process is repeated until the training reaches convergence. At the end, the algorithm takes the model with the highest score without retraining.<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
For LFW, there is not a noticeable difference between the algorithms proposed in this paper and the other algorithms. However, AM-Softmax achieved higher results than Search-Softmax. Random-Softmax achieved the highest results by 0.03%.<br />
<br />
Random-Softmax outperforms baseline Soft-max and is comparable to most of the margin-based softmax. Search-Softmax boost the performance and better most methods specifically when training CASIA-WebFace-R data set, it achieves 0.72% average improvement over AM-Softmax. The reason the model proposed by the paper gives better results is because of their optimization strategy which helps boost the discimination power. Also the sampled candidate from the paper’s proposed search space can well approximate the margin-based loss functions. More tests need to happen to more complicated protocols to test the performance further. Not a lot of improvement has been shown on those test sets, since they are relatively simple and the performance of all the methods on these test sets are near saturation. <br />
<br />
<center>Table 1.Verification performance (%) of different methods on the test sets LFW, SLLFW, CALFW, CPLFW, AgeDB and CFP. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<br />
<center>[[Image:G25_Table1.png|900px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on RFW ===<br />
The RFW dataset measures racial bias which consists of Caucasian, Indian, Asian, and African. Using this as the test set, Random-softmax and Search-softmax performed better than the other methods. Random-softmax outperforms the baseline softmax by a large margin which means reducing the softmax probability will enhance the feature discrimination for face recognition. It is also observed that the reward guided search-softmax method is more likely to enhance the discriminative feature learning resulting in higher performance as shown in Table 2 and Table 3. <br />
<br />
<center>Table 2. Verification performance (%) of different methods on the test set RFW. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table2.png|500px |alt=Alt text|Title text]]</center><br />
<br />
<br />
<center>Table 3. Verification performance (%) of different methods on the test set RFW. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table3.png|500px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
The different loss functions are tested again with more complicated protocols. The identification (Id.) Rank-1 and the verification (Veri.) with the true positive rate (TPR) at low false acceptance rate (FAR) at <math>1e-3</math> on MegaFace, the identification TPR@FAR = <math>1e-6</math> and the verification TPR@FAR = <math>1e-9</math> on Trillion-Pairs are reported on Table 4 and 5.<br />
<br />
On the test sets MegaFace and Trillion-Pairs, Search-softmax achieves the best performance over all other alternative methods. On MegaFace, Search-softmax beat the best competitor AM-softmax by a large margin. It also outperformed AM-LFS due to new designed search space. <br />
<br />
<center>Table 4. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table4.png|450px |alt=Alt text|Title text]]</center><br />
<br />
<br />
<center>Table 5. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table5.png|450px |alt=Alt text|Title text]]</center><br />
<br />
From the CMC curves and ROC curves in Figure 2, similar trends are observed at other measures. There is a same trend on Trillion-Pairs where Search-softmax loss is found to be superior with 4% improvements with CASIA-WebFace-R and 1% improvements with MS-Celeb-1M-v1c-R at both the identification and verification. Based on these experiments, Search-Softmax loss can perform well, especially with a low false positive rate and it shows a strong generalization ability for face recognition.<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
== Critiques ==<br />
* Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
* Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
* AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
* The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46851Loss Function Search for Face Recognition2020-11-26T21:54:00Z<p>Jcllau: /* Introduction */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and <math>s</math> represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
<center>[[Image:G25_Figure1.png|300px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]</center><br />
<center>Figure 1: Reinforcement Learning scenario [4]</center><br />
<br />
The reward function is what guides the agent to move into a certain direction. As mentioned above, the system receives feedback from the data to achieve the best outcome. This is caused by the reward being edited based on the feedback it receives when a task is completed [5]. <br />
<br />
In this paper, RL is being used to generate a distribution of the hyperparameter <math>\mu</math> for the SoftMax equation using the reward function. <math>\mu</math> updates after each epoch from the reward function. <br />
<br />
<center><math>\mu_{e+1}=\mu_e + \eta \frac{1}{B} \sum_{i=1}^B R{(a_i)}{\nabla_a}log{(g(a_i;\mu,\sigma))}</math></center><br />
<br />
=== Optimization ===<br />
Calculating the reward involves a standard bi-level optimization problem, which involves a hyperparameter ({<math>a_1,a_2,…,a_B</math>}) that can be used for minimizing one objective function while maximizing another objective function simultaneously:<br />
<br />
<center><math>max_a R(a)=r(M_{w^*(a)},S_v)</math></center><br />
<center><math>w^*(a)=_w \sum_{(x,y) \in S_t} L^a (M_w(x),y)</math></center><br />
<br />
In this case, the loss function takes the training set St and the reward function takes the validation set <math>S_v</math>. The weights <math>w</math> are trained such that the loss function is minimized while the reward function is maximized. The calculated reward for each model ({<math>M_{we1},M_{we2},…,M_{weB}</math>}) yields the corresponding score, then the algorithm chooses the one with the highest score for model index selection. With the model containing the highest score being used in the next epoch, this process is repeated until the training reaches convergence. At the end, the algorithm takes the model with the highest score without retraining.<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
For LFW, there is not a noticeable difference between the algorithms proposed in this paper and the other algorithms. However, AM-Softmax achieved higher results than Search-Softmax. Random-Softmax achieved the highest results by 0.03%.<br />
<br />
Random-Softmax outperforms baseline Soft-max and is comparable to most of the margin-based softmax. Search-Softmax boost the performance and better most methods specifically when training CASIA-WebFace-R data set, it achieves 0.72% average improvement over AM-Softmax. The reason the model proposed by the paper gives better results is because of their optimization strategy which helps boost the discimination power. Also the sampled candidate from the paper’s proposed search space can well approximate the margin-based loss functions. More tests need to happen to more complicated protocols to test the performance further. Not a lot of improvement has been shown on those test sets, since they are relatively simple and the performance of all the methods on these test sets are near saturation. <br />
<br />
<center>Table 1.Verification performance (%) of different methods on the test sets LFW, SLLFW, CALFW, CPLFW, AgeDB and CFP. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<br />
<center>[[Image:G25_Table1.png|900px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on RFW ===<br />
The RFW dataset measures racial bias which consists of Caucasian, Indian, Asian, and African. Using this as the test set, Random-softmax and Search-softmax performed better than the other methods. Random-softmax outperforms the baseline softmax by a large margin which means reducing the softmax probability will enhance the feature discrimination for face recognition. It is also observed that the reward guided search-softmax method is more likely to enhance the discriminative feature learning resulting in higher performance as shown in Table 2 and Table 3. <br />
<br />
<center>Table 2. Verification performance (%) of different methods on the test set RFW. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table2.png|500px |alt=Alt text|Title text]]</center><br />
<br />
<br />
<center>Table 3. Verification performance (%) of different methods on the test set RFW. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table3.png|500px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
The different loss functions are tested again with more complicated protocols. The identification (Id.) Rank-1 and the verification (Veri.) with the true positive rate (TPR) at low false acceptance rate (FAR) at <math>1e-3</math> on MegaFace, the identification TPR@FAR = <math>1e-6</math> and the verification TPR@FAR = <math>1e-9</math> on Trillion-Pairs are reported on Table 4 and 5.<br />
<br />
On the test sets MegaFace and Trillion-Pairs, Search-softmax achieves the best performance over all other alternative methods. On MegaFace, Search-softmax beat the best competitor AM-softmax by a large margin. It also outperformed AM-LFS due to new designed search space. <br />
<br />
<center>Table 4. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table4.png|450px |alt=Alt text|Title text]]</center><br />
<br />
<br />
<center>Table 5. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table5.png|450px |alt=Alt text|Title text]]</center><br />
<br />
From the CMC curves and ROC curves in Figure 2, similar trends are observed at other measures. There is a same trend on Trillion-Pairs where Search-softmax loss is found to be superior with 4% improvements with CASIA-WebFace-R and 1% improvements with MS-Celeb-1M-v1c-R at both the identification and verification. Based on these experiments, Search-Softmax loss can perform well, especially with a low false positive rate and it shows a strong generalization ability for face recognition.<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
* Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
* Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
* AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
* The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46850Loss Function Search for Face Recognition2020-11-26T21:36:46Z<p>Jcllau: /* Critiques */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
<center>[[Image:G25_Figure1.png|300px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]</center><br />
<center>Figure 1: Reinforcement Learning scenario [4]</center><br />
<br />
The reward function is what guides the agent to move into a certain direction. As mentioned above, the system receives feedback from the data to achieve the best outcome. This is caused by the reward being edited based on the feedback it receives when a task is completed [5]. <br />
<br />
In this paper, RL is being used to generate a distribution of the hyperparameter <math>\mu</math> for the SoftMax equation using the reward function. <math>\mu</math> updates after each epoch from the reward function. <br />
<br />
<center><math>\mu_{e+1}=\mu_e + \eta \frac{1}{B} \sum_{i=1}^B R{(a_i)}{\nabla_a}log{(g(a_i;\mu,\sigma))}</math></center><br />
<br />
=== Optimization ===<br />
Calculating the reward involves a standard bi-level optimization problem, which involves a hyperparameter ({<math>a_1,a_2,…,a_B</math>}) that can be used for minimizing one objective function while maximizing another objective function simultaneously:<br />
<br />
<center><math>max_a R(a)=r(M_{w^*(a)},S_v)</math></center><br />
<center><math>w^*(a)=_w \sum_{(x,y) \in S_t} L^a (M_w(x),y)</math></center><br />
<br />
In this case, the loss function takes the training set St and the reward function takes the validation set <math>S_v</math>. The weights <math>w</math> are trained such that the loss function is minimized while the reward function is maximized. The calculated reward for each model ({<math>M_{we1},M_{we2},…,M_{weB}</math>}) yields the corresponding score, then the algorithm chooses the one with the highest score for model index selection. With the model containing the highest score being used in the next epoch, this process is repeated until the training reaches convergence. At the end, the algorithm takes the model with the highest score without retraining.<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
For LFW, there is not a noticeable difference between the algorithms proposed in this paper and the other algorithms. However, AM-Softmax achieved higher results than Search-Softmax. Random-Softmax achieved the highest results by 0.03%.<br />
<br />
Random-Softmax outperforms baseline Soft-max and is comparable to most of the margin-based softmax. Search-Softmax boost the performance and better most methods specifically when training CASIA-WebFace-R data set, it achieves 0.72% average improvement over AM-Softmax. The reason the model proposed by the paper gives better results is because of their optimization strategy which helps boost the discimination power. Also the sampled candidate from the paper’s proposed search space can well approximate the margin-based loss functions. More tests need to happen to more complicated protocols to test the performance further. Not a lot of improvement has been shown on those test sets, since they are relatively simple and the performance of all the methods on these test sets are near saturation. <br />
<br />
<center>Table 1.Verification performance (%) of different methods on the test sets LFW, SLLFW, CALFW, CPLFW, AgeDB and CFP. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<br />
<center>[[Image:G25_Table1.png|900px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on RFW ===<br />
The RFW dataset measures racial bias which consists of Caucasian, Indian, Asian, and African. Using this as the test set, Random-softmax and Search-softmax performed better than the other methods. Random-softmax outperforms the baseline softmax by a large margin which means reducing the softmax probability will enhance the feature discrimination for face recognition. It is also observed that the reward guided search-softmax method is more likely to enhance the discriminative feature learning resulting in higher performance as shown in Table 2 and Table 3. <br />
<br />
<center>Table 2. Verification performance (%) of different methods on the test set RFW. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table2.png|500px |alt=Alt text|Title text]]</center><br />
<br />
<br />
<center>Table 3. Verification performance (%) of different methods on the test set RFW. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table3.png|500px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
The different loss functions are tested again with more complicated protocols. The identification (Id.) Rank-1 and the verification (Veri.) with the true positive rate (TPR) at low false acceptance rate (FAR) at <math>1e-3</math> on MegaFace, the identification TPR@FAR = <math>1e-6</math> and the verification TPR@FAR = <math>1e-9</math> on Trillion-Pairs are reported on Table 4 and 5.<br />
<br />
On the test sets MegaFace and Trillion-Pairs, Search-softmax achieves the best performance over all other alternative methods. On MegaFace, Search-softmax beat the best competitor AM-softmax by a large margin. It also outperformed AM-LFS due to new designed search space. <br />
<br />
<center>Table 4. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table4.png|450px |alt=Alt text|Title text]]</center><br />
<br />
<br />
<center>Table 5. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table5.png|450px |alt=Alt text|Title text]]</center><br />
<br />
From the CMC curves and ROC curves in Figure 2, similar trends are observed at other measures. There is a same trend on Trillion-Pairs where Search-softmax loss is found to be superior with 4% improvements with CASIA-WebFace-R and 1% improvements with MS-Celeb-1M-v1c-R at both the identification and verification. Based on these experiments, Search-Softmax loss can perform well, especially with a low false positive rate and it shows a strong generalization ability for face recognition.<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
* Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
* Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
* AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
* The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46848Loss Function Search for Face Recognition2020-11-26T21:29:24Z<p>Jcllau: /* Results on MegaFace and Trillion-Pairs */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
<center>[[Image:G25_Figure1.png|300px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]</center><br />
<center>Figure 1: Reinforcement Learning scenario [4]</center><br />
<br />
The reward function is what guides the agent to move into a certain direction. As mentioned above, the system receives feedback from the data to achieve the best outcome. This is caused by the reward being edited based on the feedback it receives when a task is completed [5]. <br />
<br />
In this paper, RL is being used to generate a distribution of the hyperparameter <math>\mu</math> for the SoftMax equation using the reward function. <math>\mu</math> updates after each epoch from the reward function. <br />
<br />
<center><math>\mu_{e+1}=\mu_e + \eta \frac{1}{B} \sum_{i=1}^B R{(a_i)}{\nabla_a}log{(g(a_i;\mu,\sigma))}</math></center><br />
<br />
=== Optimization ===<br />
Calculating the reward involves a standard bi-level optimization problem, which involves a hyperparameter ({<math>a_1,a_2,…,a_B</math>}) that can be used for minimizing one objective function while maximizing another objective function simultaneously:<br />
<br />
<center><math>max_a R(a)=r(M_{w^*(a)},S_v)</math></center><br />
<center><math>w^*(a)=_w \sum_{(x,y) \in S_t} L^a (M_w(x),y)</math></center><br />
<br />
In this case, the loss function takes the training set St and the reward function takes the validation set <math>S_v</math>. The weights <math>w</math> are trained such that the loss function is minimized while the reward function is maximized. The calculated reward for each model ({<math>M_{we1},M_{we2},…,M_{weB}</math>}) yields the corresponding score, then the algorithm chooses the one with the highest score for model index selection. With the model containing the highest score being used in the next epoch, this process is repeated until the training reaches convergence. At the end, the algorithm takes the model with the highest score without retraining.<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
For LFW, there is not a noticeable difference between the algorithms proposed in this paper and the other algorithms. However, AM-Softmax achieved higher results than Search-Softmax. Random-Softmax achieved the highest results by 0.03%.<br />
<br />
Random-Softmax outperforms baseline Soft-max and is comparable to most of the margin-based softmax. Search-Softmax boost the performance and better most methods specifically when training CASIA-WebFace-R data set, it achieves 0.72% average improvement over AM-Softmax. The reason the model proposed by the paper gives better results is because of their optimization strategy which helps boost the discimination power. Also the sampled candidate from the paper’s proposed search space can well approximate the margin-based loss functions. More tests need to happen to more complicated protocols to test the performance further. Not a lot of improvement has been shown on those test sets, since they are relatively simple and the performance of all the methods on these test sets are near saturation. <br />
<br />
<center>Table 1.Verification performance (%) of different methods on the test sets LFW, SLLFW, CALFW, CPLFW, AgeDB and CFP. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<br />
<center>[[Image:G25_Table1.png|900px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on RFW ===<br />
The RFW dataset measures racial bias which consists of Caucasian, Indian, Asian, and African. Using this as the test set, Random-softmax and Search-softmax performed better than the other methods. Random-softmax outperforms the baseline softmax by a large margin which means reducing the softmax probability will enhance the feature discrimination for face recognition. It is also observed that the reward guided search-softmax method is more likely to enhance the discriminative feature learning resulting in higher performance as shown in Table 2 and Table 3. <br />
<br />
<center>Table 2. Verification performance (%) of different methods on the test set RFW. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table2.png|500px |alt=Alt text|Title text]]</center><br />
<br />
<br />
<center>Table 3. Verification performance (%) of different methods on the test set RFW. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table3.png|500px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
The different loss functions are tested again with more complicated protocols. The identification (Id.) Rank-1 and the verification (Veri.) with the true positive rate (TPR) at low false acceptance rate (FAR) at <math>1e-3</math> on MegaFace, the identification TPR@FAR = <math>1e-6</math> and the verification TPR@FAR = <math>1e-9</math> on Trillion-Pairs are reported on Table 4 and 5.<br />
<br />
On the test sets MegaFace and Trillion-Pairs, Search-softmax achieves the best performance over all other alternative methods. On MegaFace, Search-softmax beat the best competitor AM-softmax by a large margin. It also outperformed AM-LFS due to new designed search space. <br />
<br />
<center>Table 4. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table4.png|450px |alt=Alt text|Title text]]</center><br />
<br />
<br />
<center>Table 5. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table5.png|450px |alt=Alt text|Title text]]</center><br />
<br />
From the CMC curves and ROC curves in Figure 2, similar trends are observed at other measures. There is a same trend on Trillion-Pairs where Search-softmax loss is found to be superior with 4% improvements with CASIA-WebFace-R and 1% improvements with MS-Celeb-1M-v1c-R at both the identification and verification. Based on these experiments, Search-Softmax loss can perform well, especially with a low false positive rate and it shows a strong generalization ability for face recognition.<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46847Loss Function Search for Face Recognition2020-11-26T21:29:01Z<p>Jcllau: /* Results on MegaFace and Trillion-Pairs */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
<center>[[Image:G25_Figure1.png|300px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]</center><br />
<center>Figure 1: Reinforcement Learning scenario [4]</center><br />
<br />
The reward function is what guides the agent to move into a certain direction. As mentioned above, the system receives feedback from the data to achieve the best outcome. This is caused by the reward being edited based on the feedback it receives when a task is completed [5]. <br />
<br />
In this paper, RL is being used to generate a distribution of the hyperparameter <math>\mu</math> for the SoftMax equation using the reward function. <math>\mu</math> updates after each epoch from the reward function. <br />
<br />
<center><math>\mu_{e+1}=\mu_e + \eta \frac{1}{B} \sum_{i=1}^B R{(a_i)}{\nabla_a}log{(g(a_i;\mu,\sigma))}</math></center><br />
<br />
=== Optimization ===<br />
Calculating the reward involves a standard bi-level optimization problem, which involves a hyperparameter ({<math>a_1,a_2,…,a_B</math>}) that can be used for minimizing one objective function while maximizing another objective function simultaneously:<br />
<br />
<center><math>max_a R(a)=r(M_{w^*(a)},S_v)</math></center><br />
<center><math>w^*(a)=_w \sum_{(x,y) \in S_t} L^a (M_w(x),y)</math></center><br />
<br />
In this case, the loss function takes the training set St and the reward function takes the validation set <math>S_v</math>. The weights <math>w</math> are trained such that the loss function is minimized while the reward function is maximized. The calculated reward for each model ({<math>M_{we1},M_{we2},…,M_{weB}</math>}) yields the corresponding score, then the algorithm chooses the one with the highest score for model index selection. With the model containing the highest score being used in the next epoch, this process is repeated until the training reaches convergence. At the end, the algorithm takes the model with the highest score without retraining.<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
For LFW, there is not a noticeable difference between the algorithms proposed in this paper and the other algorithms. However, AM-Softmax achieved higher results than Search-Softmax. Random-Softmax achieved the highest results by 0.03%.<br />
<br />
Random-Softmax outperforms baseline Soft-max and is comparable to most of the margin-based softmax. Search-Softmax boost the performance and better most methods specifically when training CASIA-WebFace-R data set, it achieves 0.72% average improvement over AM-Softmax. The reason the model proposed by the paper gives better results is because of their optimization strategy which helps boost the discimination power. Also the sampled candidate from the paper’s proposed search space can well approximate the margin-based loss functions. More tests need to happen to more complicated protocols to test the performance further. Not a lot of improvement has been shown on those test sets, since they are relatively simple and the performance of all the methods on these test sets are near saturation. <br />
<br />
<center>Table 1.Verification performance (%) of different methods on the test sets LFW, SLLFW, CALFW, CPLFW, AgeDB and CFP. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<br />
<center>[[Image:G25_Table1.png|900px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on RFW ===<br />
The RFW dataset measures racial bias which consists of Caucasian, Indian, Asian, and African. Using this as the test set, Random-softmax and Search-softmax performed better than the other methods. Random-softmax outperforms the baseline softmax by a large margin which means reducing the softmax probability will enhance the feature discrimination for face recognition. It is also observed that the reward guided search-softmax method is more likely to enhance the discriminative feature learning resulting in higher performance as shown in Table 2 and Table 3. <br />
<br />
<center>Table 2. Verification performance (%) of different methods on the test set RFW. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table2.png|500px |alt=Alt text|Title text]]</center><br />
<br />
<br />
<center>Table 3. Verification performance (%) of different methods on the test set RFW. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table3.png|500px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
The different loss functions are tested again with more complicated protocols. The identification (Id.) Rank-1 and the verification (Veri.) with the true positive rate (TPR) at low false acceptance rate (FAR) at <math>1e-3</math> on MegaFace, the identification TPR@FAR = <math>1e-6</math> and the verification TPR@FAR = <math>1e-9</math> on Trillion-Pairs are reported on Table 4 and 5.<br />
<br />
On the test sets MegaFace and Trillion-Pairs, Search-softmax achieves the best performance over all other alternative methods. On MegaFace, Search-softmax beat the best competitor AM-softmax by a large margin. It also outperformed AM-LFS due to new designed search space. <br />
<br />
<center>Table 4. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table4.png|450px |alt=Alt text|Title text]]</center><br />
<br />
<center>Table 5. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table5.png|450px |alt=Alt text|Title text]]</center><br />
<br />
From the CMC curves and ROC curves in Figure 2, similar trends are observed at other measures. There is a same trend on Trillion-Pairs where Search-softmax loss is found to be superior with 4% improvements with CASIA-WebFace-R and 1% improvements with MS-Celeb-1M-v1c-R at both the identification and verification. Based on these experiments, Search-Softmax loss can perform well, especially with a low false positive rate and it shows a strong generalization ability for face recognition.<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:G25_Table5.png&diff=46846File:G25 Table5.png2020-11-26T21:28:24Z<p>Jcllau: </p>
<hr />
<div></div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:G25_Table4.png&diff=46844File:G25 Table4.png2020-11-26T21:27:21Z<p>Jcllau: </p>
<hr />
<div></div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46843Loss Function Search for Face Recognition2020-11-26T21:27:12Z<p>Jcllau: /* Results on MegaFace and Trillion-Pairs */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
<center>[[Image:G25_Figure1.png|300px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]</center><br />
<center>Figure 1: Reinforcement Learning scenario [4]</center><br />
<br />
The reward function is what guides the agent to move into a certain direction. As mentioned above, the system receives feedback from the data to achieve the best outcome. This is caused by the reward being edited based on the feedback it receives when a task is completed [5]. <br />
<br />
In this paper, RL is being used to generate a distribution of the hyperparameter <math>\mu</math> for the SoftMax equation using the reward function. <math>\mu</math> updates after each epoch from the reward function. <br />
<br />
<center><math>\mu_{e+1}=\mu_e + \eta \frac{1}{B} \sum_{i=1}^B R{(a_i)}{\nabla_a}log{(g(a_i;\mu,\sigma))}</math></center><br />
<br />
=== Optimization ===<br />
Calculating the reward involves a standard bi-level optimization problem, which involves a hyperparameter ({<math>a_1,a_2,…,a_B</math>}) that can be used for minimizing one objective function while maximizing another objective function simultaneously:<br />
<br />
<center><math>max_a R(a)=r(M_{w^*(a)},S_v)</math></center><br />
<center><math>w^*(a)=_w \sum_{(x,y) \in S_t} L^a (M_w(x),y)</math></center><br />
<br />
In this case, the loss function takes the training set St and the reward function takes the validation set <math>S_v</math>. The weights <math>w</math> are trained such that the loss function is minimized while the reward function is maximized. The calculated reward for each model ({<math>M_{we1},M_{we2},…,M_{weB}</math>}) yields the corresponding score, then the algorithm chooses the one with the highest score for model index selection. With the model containing the highest score being used in the next epoch, this process is repeated until the training reaches convergence. At the end, the algorithm takes the model with the highest score without retraining.<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
For LFW, there is not a noticeable difference between the algorithms proposed in this paper and the other algorithms. However, AM-Softmax achieved higher results than Search-Softmax. Random-Softmax achieved the highest results by 0.03%.<br />
<br />
Random-Softmax outperforms baseline Soft-max and is comparable to most of the margin-based softmax. Search-Softmax boost the performance and better most methods specifically when training CASIA-WebFace-R data set, it achieves 0.72% average improvement over AM-Softmax. The reason the model proposed by the paper gives better results is because of their optimization strategy which helps boost the discimination power. Also the sampled candidate from the paper’s proposed search space can well approximate the margin-based loss functions. More tests need to happen to more complicated protocols to test the performance further. Not a lot of improvement has been shown on those test sets, since they are relatively simple and the performance of all the methods on these test sets are near saturation. <br />
<br />
<center>Table 1.Verification performance (%) of different methods on the test sets LFW, SLLFW, CALFW, CPLFW, AgeDB and CFP. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<br />
<center>[[Image:G25_Table1.png|900px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on RFW ===<br />
The RFW dataset measures racial bias which consists of Caucasian, Indian, Asian, and African. Using this as the test set, Random-softmax and Search-softmax performed better than the other methods. Random-softmax outperforms the baseline softmax by a large margin which means reducing the softmax probability will enhance the feature discrimination for face recognition. It is also observed that the reward guided search-softmax method is more likely to enhance the discriminative feature learning resulting in higher performance as shown in Table 2 and Table 3. <br />
<br />
<center>Table 2. Verification performance (%) of different methods on the test set RFW. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table2.png|500px |alt=Alt text|Title text]]</center><br />
<br />
<br />
<center>Table 3. Verification performance (%) of different methods on the test set RFW. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table3.png|500px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
The different loss functions are tested again with more complicated protocols. The identification (Id.) Rank-1 and the verification (Veri.) with the true positive rate (TPR) at low false acceptance rate (FAR) at <math>1e-3</math> on MegaFace, the identification TPR@FAR = <math>1e-6</math> and the verification TPR@FAR = <math>1e-9</math> on Trillion-Pairs are reported on Table 4 and 5.<br />
<br />
On the test sets MegaFace and Trillion-Pairs, Search-softmax achieves the best performance over all other alternative methods. On MegaFace, Search-softmax beat the best competitor AM-softmax by a large margin. It also outperformed AM-LFS due to new designed search space. <br />
<br />
<center>Table 4. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table4.png|500px |alt=Alt text|Title text]]</center><br />
<br />
<center>Table 5. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table5.png|500px |alt=Alt text|Title text]]</center><br />
<br />
From the CMC curves and ROC curves in Figure 2, similar trends are observed at other measures. There is a same trend on Trillion-Pairs where Search-softmax loss is found to be superior with 4% improvements with CASIA-WebFace-R and 1% improvements with MS-Celeb-1M-v1c-R at both the identification and verification. Based on these experiments, Search-Softmax loss can perform well, especially with a low false positive rate and it shows a strong generalization ability for face recognition.<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46837Loss Function Search for Face Recognition2020-11-26T21:17:54Z<p>Jcllau: /* Results on RFW */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
<center>[[Image:G25_Figure1.png|300px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]</center><br />
<center>Figure 1: Reinforcement Learning scenario [4]</center><br />
<br />
The reward function is what guides the agent to move into a certain direction. As mentioned above, the system receives feedback from the data to achieve the best outcome. This is caused by the reward being edited based on the feedback it receives when a task is completed [5]. <br />
<br />
In this paper, RL is being used to generate a distribution of the hyperparameter <math>\mu</math> for the SoftMax equation using the reward function. <math>\mu</math> updates after each epoch from the reward function. <br />
<br />
<center><math>\mu_{e+1}=\mu_e + \eta \frac{1}{B} \sum_{i=1}^B R{(a_i)}{\nabla_a}log{(g(a_i;\mu,\sigma))}</math></center><br />
<br />
=== Optimization ===<br />
Calculating the reward involves a standard bi-level optimization problem, which involves a hyperparameter ({<math>a_1,a_2,…,a_B</math>}) that can be used for minimizing one objective function while maximizing another objective function simultaneously:<br />
<br />
<center><math>max_a R(a)=r(M_{w^*(a)},S_v)</math></center><br />
<center><math>w^*(a)=_w \sum_{(x,y) \in S_t} L^a (M_w(x),y)</math></center><br />
<br />
In this case, the loss function takes the training set St and the reward function takes the validation set <math>S_v</math>. The weights <math>w</math> are trained such that the loss function is minimized while the reward function is maximized. The calculated reward for each model ({<math>M_{we1},M_{we2},…,M_{weB}</math>}) yields the corresponding score, then the algorithm chooses the one with the highest score for model index selection. With the model containing the highest score being used in the next epoch, this process is repeated until the training reaches convergence. At the end, the algorithm takes the model with the highest score without retraining.<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
For LFW, there is not a noticeable difference between the algorithms proposed in this paper and the other algorithms. However, AM-Softmax achieved higher results than Search-Softmax. Random-Softmax achieved the highest results by 0.03%.<br />
<br />
Random-Softmax outperforms baseline Soft-max and is comparable to most of the margin-based softmax. Search-Softmax boost the performance and better most methods specifically when training CASIA-WebFace-R data set, it achieves 0.72% average improvement over AM-Softmax. The reason the model proposed by the paper gives better results is because of their optimization strategy which helps boost the discimination power. Also the sampled candidate from the paper’s proposed search space can well approximate the margin-based loss functions. More tests need to happen to more complicated protocols to test the performance further. Not a lot of improvement has been shown on those test sets, since they are relatively simple and the performance of all the methods on these test sets are near saturation. <br />
<br />
<center>Table 1.Verification performance (%) of different methods on the test sets LFW, SLLFW, CALFW, CPLFW, AgeDB and CFP. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<br />
<center>[[Image:G25_Table1.png|900px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on RFW ===<br />
The RFW dataset measures racial bias which consists of Caucasian, Indian, Asian, and African. Using this as the test set, Random-softmax and Search-softmax performed better than the other methods. Random-softmax outperforms the baseline softmax by a large margin which means reducing the softmax probability will enhance the feature discrimination for face recognition. It is also observed that the reward guided search-softmax method is more likely to enhance the discriminative feature learning resulting in higher performance as shown in Table 2 and Table 3. <br />
<br />
<center>Table 2. Verification performance (%) of different methods on the test set RFW. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table2.png|500px |alt=Alt text|Title text]]</center><br />
<br />
<br />
<center>Table 3. Verification performance (%) of different methods on the test set RFW. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table3.png|500px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:G25_Table3.png&diff=46835File:G25 Table3.png2020-11-26T21:16:58Z<p>Jcllau: </p>
<hr />
<div></div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:G25_Table2.png&diff=46832File:G25 Table2.png2020-11-26T21:16:27Z<p>Jcllau: </p>
<hr />
<div></div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46830Loss Function Search for Face Recognition2020-11-26T21:16:07Z<p>Jcllau: /* Results on RFW */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
<center>[[Image:G25_Figure1.png|300px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]</center><br />
<center>Figure 1: Reinforcement Learning scenario [4]</center><br />
<br />
The reward function is what guides the agent to move into a certain direction. As mentioned above, the system receives feedback from the data to achieve the best outcome. This is caused by the reward being edited based on the feedback it receives when a task is completed [5]. <br />
<br />
In this paper, RL is being used to generate a distribution of the hyperparameter <math>\mu</math> for the SoftMax equation using the reward function. <math>\mu</math> updates after each epoch from the reward function. <br />
<br />
<center><math>\mu_{e+1}=\mu_e + \eta \frac{1}{B} \sum_{i=1}^B R{(a_i)}{\nabla_a}log{(g(a_i;\mu,\sigma))}</math></center><br />
<br />
=== Optimization ===<br />
Calculating the reward involves a standard bi-level optimization problem, which involves a hyperparameter ({<math>a_1,a_2,…,a_B</math>}) that can be used for minimizing one objective function while maximizing another objective function simultaneously:<br />
<br />
<center><math>max_a R(a)=r(M_{w^*(a)},S_v)</math></center><br />
<center><math>w^*(a)=_w \sum_{(x,y) \in S_t} L^a (M_w(x),y)</math></center><br />
<br />
In this case, the loss function takes the training set St and the reward function takes the validation set <math>S_v</math>. The weights <math>w</math> are trained such that the loss function is minimized while the reward function is maximized. The calculated reward for each model ({<math>M_{we1},M_{we2},…,M_{weB}</math>}) yields the corresponding score, then the algorithm chooses the one with the highest score for model index selection. With the model containing the highest score being used in the next epoch, this process is repeated until the training reaches convergence. At the end, the algorithm takes the model with the highest score without retraining.<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
For LFW, there is not a noticeable difference between the algorithms proposed in this paper and the other algorithms. However, AM-Softmax achieved higher results than Search-Softmax. Random-Softmax achieved the highest results by 0.03%.<br />
<br />
Random-Softmax outperforms baseline Soft-max and is comparable to most of the margin-based softmax. Search-Softmax boost the performance and better most methods specifically when training CASIA-WebFace-R data set, it achieves 0.72% average improvement over AM-Softmax. The reason the model proposed by the paper gives better results is because of their optimization strategy which helps boost the discimination power. Also the sampled candidate from the paper’s proposed search space can well approximate the margin-based loss functions. More tests need to happen to more complicated protocols to test the performance further. Not a lot of improvement has been shown on those test sets, since they are relatively simple and the performance of all the methods on these test sets are near saturation. <br />
<br />
<center>Table 1.Verification performance (%) of different methods on the test sets LFW, SLLFW, CALFW, CPLFW, AgeDB and CFP. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<br />
<center>[[Image:G25_Table1.png|900px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on RFW ===<br />
The RFW dataset measures racial bias which consists of Caucasian, Indian, Asian, and African. Using this as the test set, Random-softmax and Search-softmax performed better than the other methods. Random-softmax outperforms the baseline softmax by a large margin which means reducing the softmax probability will enhance the feature discrimination for face recognition. It is also observed that the reward guided search-softmax method is more likely to enhance the discriminative feature learning resulting in higher performance as shown in Table 2 and Table 3. <br />
<br />
<center>Table 2. Verification performance (%) of different methods on the test set RFW. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<center>[[Image:G25_Table2.png|900px |alt=Alt text|Title text]]</center><br />
<br />
<center>Table 3. Verification performance (%) of different methods on the test set RFW. The training set is '''MS-Celeb-1M-v1c-R''' [1].</center><br />
<center>[[Image:G25_Table3.png|900px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46828Loss Function Search for Face Recognition2020-11-26T21:14:09Z<p>Jcllau: /* Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
<center>[[Image:G25_Figure1.png|300px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]</center><br />
<center>Figure 1: Reinforcement Learning scenario [4]</center><br />
<br />
The reward function is what guides the agent to move into a certain direction. As mentioned above, the system receives feedback from the data to achieve the best outcome. This is caused by the reward being edited based on the feedback it receives when a task is completed [5]. <br />
<br />
In this paper, RL is being used to generate a distribution of the hyperparameter <math>\mu</math> for the SoftMax equation using the reward function. <math>\mu</math> updates after each epoch from the reward function. <br />
<br />
<center><math>\mu_{e+1}=\mu_e + \eta \frac{1}{B} \sum_{i=1}^B R{(a_i)}{\nabla_a}log{(g(a_i;\mu,\sigma))}</math></center><br />
<br />
=== Optimization ===<br />
Calculating the reward involves a standard bi-level optimization problem, which involves a hyperparameter ({<math>a_1,a_2,…,a_B</math>}) that can be used for minimizing one objective function while maximizing another objective function simultaneously:<br />
<br />
<center><math>max_a R(a)=r(M_{w^*(a)},S_v)</math></center><br />
<center><math>w^*(a)=_w \sum_{(x,y) \in S_t} L^a (M_w(x),y)</math></center><br />
<br />
In this case, the loss function takes the training set St and the reward function takes the validation set <math>S_v</math>. The weights <math>w</math> are trained such that the loss function is minimized while the reward function is maximized. The calculated reward for each model ({<math>M_{we1},M_{we2},…,M_{weB}</math>}) yields the corresponding score, then the algorithm chooses the one with the highest score for model index selection. With the model containing the highest score being used in the next epoch, this process is repeated until the training reaches convergence. At the end, the algorithm takes the model with the highest score without retraining.<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
For LFW, there is not a noticeable difference between the algorithms proposed in this paper and the other algorithms. However, AM-Softmax achieved higher results than Search-Softmax. Random-Softmax achieved the highest results by 0.03%.<br />
<br />
Random-Softmax outperforms baseline Soft-max and is comparable to most of the margin-based softmax. Search-Softmax boost the performance and better most methods specifically when training CASIA-WebFace-R data set, it achieves 0.72% average improvement over AM-Softmax. The reason the model proposed by the paper gives better results is because of their optimization strategy which helps boost the discimination power. Also the sampled candidate from the paper’s proposed search space can well approximate the margin-based loss functions. More tests need to happen to more complicated protocols to test the performance further. Not a lot of improvement has been shown on those test sets, since they are relatively simple and the performance of all the methods on these test sets are near saturation. <br />
<br />
<center>Table 1.Verification performance (%) of different methods on the test sets LFW, SLLFW, CALFW, CPLFW, AgeDB and CFP. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<br />
<center>[[Image:G25_Table1.png|900px |alt=Alt text|Title text]]</center><br />
<br />
=== Results on RFW ===<br />
<br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46827Loss Function Search for Face Recognition2020-11-26T21:12:21Z<p>Jcllau: /* Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
<center>[[Image:G25_Figure1.png|300px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]</center><br />
<center>Figure 1: Reinforcement Learning scenario [4]</center><br />
<br />
The reward function is what guides the agent to move into a certain direction. As mentioned above, the system receives feedback from the data to achieve the best outcome. This is caused by the reward being edited based on the feedback it receives when a task is completed [5]. <br />
<br />
In this paper, RL is being used to generate a distribution of the hyperparameter <math>\mu</math> for the SoftMax equation using the reward function. <math>\mu</math> updates after each epoch from the reward function. <br />
<br />
<center><math>\mu_{e+1}=\mu_e + \eta \frac{1}{B} \sum_{i=1}^B R{(a_i)}{\nabla_a}log{(g(a_i;\mu,\sigma))}</math></center><br />
<br />
=== Optimization ===<br />
Calculating the reward involves a standard bi-level optimization problem, which involves a hyperparameter ({<math>a_1,a_2,…,a_B</math>}) that can be used for minimizing one objective function while maximizing another objective function simultaneously:<br />
<br />
<center><math>max_a R(a)=r(M_{w^*(a)},S_v)</math></center><br />
<center><math>w^*(a)=_w \sum_{(x,y) \in S_t} L^a (M_w(x),y)</math></center><br />
<br />
In this case, the loss function takes the training set St and the reward function takes the validation set <math>S_v</math>. The weights <math>w</math> are trained such that the loss function is minimized while the reward function is maximized. The calculated reward for each model ({<math>M_{we1},M_{we2},…,M_{weB}</math>}) yields the corresponding score, then the algorithm chooses the one with the highest score for model index selection. With the model containing the highest score being used in the next epoch, this process is repeated until the training reaches convergence. At the end, the algorithm takes the model with the highest score without retraining.<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
For LFW, there is not a noticeable difference between the algorithms proposed in this paper and the other algorithms. However, AM-Softmax achieved higher results than Search-Softmax. Random-Softmax achieved the highest results by 0.03%.<br />
<br />
Random-Softmax outperforms baseline Soft-max and is comparable to most of the margin-based softmax. Search-Softmax boost the performance and better most methods specifically when training CASIA-WebFace-R data set, it achieves 0.72% average improvement over AM-Softmax. The reason the model proposed by the paper gives better results is because of their optimization strategy which helps boost the discimination power. Also the sampled candidate from the paper’s proposed search space can well approximate the margin-based loss functions. More tests need to happen to more complicated protocols to test the performance further. Not a lot of improvement has been shown on those test sets, since they are relatively simple and the performance of all the methods on these test sets are near saturation. <br />
<br />
<center>Table 1.Verification performance (%) of different methods on the test sets LFW, SLLFW, CALFW, CPLFW, AgeDB and CFP. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<br />
<br />
[[File:G25_Table1.png] | 300px ]<br />
<br />
=== Results on RFW ===<br />
<br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:G25_Table1.png&diff=46825File:G25 Table1.png2020-11-26T21:11:06Z<p>Jcllau: </p>
<hr />
<div></div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46822Loss Function Search for Face Recognition2020-11-26T21:10:47Z<p>Jcllau: /* Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
<center>[[Image:G25_Figure1.png|300px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]</center><br />
<center>Figure 1: Reinforcement Learning scenario [4]</center><br />
<br />
The reward function is what guides the agent to move into a certain direction. As mentioned above, the system receives feedback from the data to achieve the best outcome. This is caused by the reward being edited based on the feedback it receives when a task is completed [5]. <br />
<br />
In this paper, RL is being used to generate a distribution of the hyperparameter <math>\mu</math> for the SoftMax equation using the reward function. <math>\mu</math> updates after each epoch from the reward function. <br />
<br />
<center><math>\mu_{e+1}=\mu_e + \eta \frac{1}{B} \sum_{i=1}^B R{(a_i)}{\nabla_a}log{(g(a_i;\mu,\sigma))}</math></center><br />
<br />
=== Optimization ===<br />
Calculating the reward involves a standard bi-level optimization problem, which involves a hyperparameter ({<math>a_1,a_2,…,a_B</math>}) that can be used for minimizing one objective function while maximizing another objective function simultaneously:<br />
<br />
<center><math>max_a R(a)=r(M_{w^*(a)},S_v)</math></center><br />
<center><math>w^*(a)=_w \sum_{(x,y) \in S_t} L^a (M_w(x),y)</math></center><br />
<br />
In this case, the loss function takes the training set St and the reward function takes the validation set <math>S_v</math>. The weights <math>w</math> are trained such that the loss function is minimized while the reward function is maximized. The calculated reward for each model ({<math>M_{we1},M_{we2},…,M_{weB}</math>}) yields the corresponding score, then the algorithm chooses the one with the highest score for model index selection. With the model containing the highest score being used in the next epoch, this process is repeated until the training reaches convergence. At the end, the algorithm takes the model with the highest score without retraining.<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
For LFW, there is not a noticeable difference between the algorithms proposed in this paper and the other algorithms. However, AM-Softmax achieved higher results than Search-Softmax. Random-Softmax achieved the highest results by 0.03%.<br />
<br />
Random-Softmax outperforms baseline Soft-max and is comparable to most of the margin-based softmax. Search-Softmax boost the performance and better most methods specifically when training CASIA-WebFace-R data set, it achieves 0.72% average improvement over AM-Softmax. The reason the model proposed by the paper gives better results is because of their optimization strategy which helps boost the discimination power. Also the sampled candidate from the paper’s proposed search space can well approximate the margin-based loss functions. More tests need to happen to more complicated protocols to test the performance further. Not a lot of improvement has been shown on those test sets, since they are relatively simple and the performance of all the methods on these test sets are near saturation. <br />
<br />
<center>Table 1.Verification performance (%) of different methods on the test sets LFW, SLLFW, CALFW, CPLFW, AgeDB and CFP. The training set is '''CASIA-WebFace-R''' [1].</center><br />
<br />
<br />
[[File:G25_Table1.png]]<br />
<br />
=== Results on RFW ===<br />
<br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46816Loss Function Search for Face Recognition2020-11-26T21:06:05Z<p>Jcllau: /* Optimization */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
<center>[[Image:G25_Figure1.png|300px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]</center><br />
<center>Figure 1: Reinforcement Learning scenario [4]</center><br />
<br />
The reward function is what guides the agent to move into a certain direction. As mentioned above, the system receives feedback from the data to achieve the best outcome. This is caused by the reward being edited based on the feedback it receives when a task is completed [5]. <br />
<br />
In this paper, RL is being used to generate a distribution of the hyperparameter <math>\mu</math> for the SoftMax equation using the reward function. <math>\mu</math> updates after each epoch from the reward function. <br />
<br />
<center><math>\mu_{e+1}=\mu_e + \eta \frac{1}{B} \sum_{i=1}^B R{(a_i)}{\nabla_a}log{(g(a_i;\mu,\sigma))}</math></center><br />
<br />
=== Optimization ===<br />
Calculating the reward involves a standard bi-level optimization problem, which involves a hyperparameter ({<math>a_1,a_2,…,a_B</math>}) that can be used for minimizing one objective function while maximizing another objective function simultaneously:<br />
<br />
<center><math>max_a R(a)=r(M_{w^*(a)},S_v)</math></center><br />
<center><math>w^*(a)=_w \sum_{(x,y) \in S_t} L^a (M_w(x),y)</math></center><br />
<br />
In this case, the loss function takes the training set St and the reward function takes the validation set <math>S_v</math>. The weights <math>w</math> are trained such that the loss function is minimized while the reward function is maximized. The calculated reward for each model ({<math>M_{we1},M_{we2},…,M_{weB}</math>}) yields the corresponding score, then the algorithm chooses the one with the highest score for model index selection. With the model containing the highest score being used in the next epoch, this process is repeated until the training reaches convergence. At the end, the algorithm takes the model with the highest score without retraining.<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
<br />
<br />
=== Results on RFW ===<br />
<br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46809Loss Function Search for Face Recognition2020-11-26T21:00:36Z<p>Jcllau: /* Reward-Guided Search */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
<center>[[Image:G25_Figure1.png|300px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]</center><br />
<center>Figure 1: Reinforcement Learning scenario [4]</center><br />
<br />
The reward function is what guides the agent to move into a certain direction. As mentioned above, the system receives feedback from the data to achieve the best outcome. This is caused by the reward being edited based on the feedback it receives when a task is completed [5]. <br />
<br />
In this paper, RL is being used to generate a distribution of the hyperparameter <math>\mu</math> for the SoftMax equation using the reward function. <math>\mu</math> updates after each epoch from the reward function. <br />
<br />
<center><math>\mu_{e+1}=\mu_e + \eta \frac{1}{B} \sum_{i=1}^B R{(a_i)}{\nabla_a}log{(g(a_i;\mu,\sigma))}</math></center><br />
<br />
=== Optimization ===<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
<br />
<br />
=== Results on RFW ===<br />
<br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46808Loss Function Search for Face Recognition2020-11-26T20:59:47Z<p>Jcllau: /* Reward-Guided Search */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
<center>[[Image:G25_Figure1.png|300px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]</center><br />
<center>Figure 1: Reinforcement Learning scenario [4]</center><br />
<br />
The reward function is what guides the agent to move into a certain direction. As mentioned above, the system receives feedback from the data to achieve the best outcome. This is caused by the reward being edited based on the feedback it receives when a task is completed [5]. <br />
<br />
In this paper, RL is being used to generate a distribution of the hyperparameter <math>\mu</math> for the SoftMax equation using the reward function. <math>\mu</math> updates after each epoch from the reward function. <br />
<br />
<center><math>\mu_{e+1}=\mu_e + \eta \frac{1}{B} \sum_{i=1}^B R{(a_i)}{\triangledown_a}log{(g(a_i;\mu,\sigma))}</math></center><br />
<br />
=== Optimization ===<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
<br />
<br />
=== Results on RFW ===<br />
<br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:G25_Figure1.png&diff=46806File:G25 Figure1.png2020-11-26T20:55:13Z<p>Jcllau: </p>
<hr />
<div></div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46805Loss Function Search for Face Recognition2020-11-26T20:55:03Z<p>Jcllau: /* Reward-Guided Search */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
[[Image:G25_Figure1.png|150px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]<br />
<br />
=== Optimization ===<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
<br />
<br />
=== Results on RFW ===<br />
<br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46804Loss Function Search for Face Recognition2020-11-26T20:54:06Z<p>Jcllau: /* Reward-Guided Search */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
[[Image:Example2.png|150px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]<br />
<br />
=== Optimization ===<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
<br />
<br />
=== Results on RFW ===<br />
<br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46803Loss Function Search for Face Recognition2020-11-26T20:53:26Z<p>Jcllau: /* Reward-Guided Search */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
[[Image:Figure1.png|150px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]<br />
<br />
=== Optimization ===<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
<br />
<br />
=== Results on RFW ===<br />
<br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46802Loss Function Search for Face Recognition2020-11-26T20:52:39Z<p>Jcllau: /* Reward-Guided Search */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
[[Image:Example2.png|150px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]<br />
<br />
=== Optimization ===<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
<br />
<br />
=== Results on RFW ===<br />
<br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46801Loss Function Search for Face Recognition2020-11-26T20:51:57Z<p>Jcllau: /* Reward-Guided Search */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
[[File: |link: https://en.wikipedia.org/wiki/Reinforcement_learning]]<br />
<br />
=== Optimization ===<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
<br />
<br />
=== Results on RFW ===<br />
<br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46800Loss Function Search for Face Recognition2020-11-26T20:51:32Z<p>Jcllau: /* Reward-Guided Search */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
[|link: https://en.wikipedia.org/wiki/Reinforcement_learning]]<br />
<br />
=== Optimization ===<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
<br />
<br />
=== Results on RFW ===<br />
<br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46799Loss Function Search for Face Recognition2020-11-26T20:50:43Z<p>Jcllau: /* Reward-Guided Search */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
[[File:https://en.wikipedia.org/wiki/Reinforcement_learning]]<br />
<br />
=== Optimization ===<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
<br />
<br />
=== Results on RFW ===<br />
<br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46798Loss Function Search for Face Recognition2020-11-26T20:50:23Z<p>Jcllau: /* Reward-Guided Search */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
[[File:Example.jpg]]<br />
<br />
=== Optimization ===<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
<br />
<br />
=== Results on RFW ===<br />
<br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46797Loss Function Search for Face Recognition2020-11-26T20:49:42Z<p>Jcllau: /* Reward-Guided Search */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
=== Optimization ===<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
<br />
<br />
=== Results on RFW ===<br />
<br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllauhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=46796Loss Function Search for Face Recognition2020-11-26T20:48:58Z<p>Jcllau: /* Reward-Guided Search */</p>
<hr />
<div>== Presented by ==<br />
Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br />
<br />
== Introduction ==<br />
Face recognition is a technology that can label a face to a specific identity. The process involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face and another face map to the same identity. Loss functions are a method of evaluating how good the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br />
<br />
<center><math>L_1=-log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}</math> [1] </center><br />
<br />
Specifically for face recognition, <math>L_1</math> is modified such that <math>w^T_yx</math> is normalized and s represents the magnitude of <math>w^T_yx</math>:<br />
<br />
<center><math>L_2=-log\frac{e^{s cos{(\theta_{{w_y},x})}}}{e^{s cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s cos{(\theta_{{w_y},x})}}}}</math> [1] </center><br />
<br />
This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above. Some of these variations will be discussed in detail in the later sections. <br />
<br />
In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br />
<br />
== Previous Work ==<br />
Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much effort such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective [2]. It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space. <br />
<br />
<br />
== Motivation ==<br />
Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions was high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br />
<br />
To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one parameter required and an improved search space using reward-based method allows the authors to determine the best option for their loss function.<br />
<br />
<br />
== Problem Formulation ==<br />
=== Analysis of Margin-based Softmax Loss ===<br />
Based on the softmax probability and the margin-based softmax probability, the following function can be developed [1]:<br />
<br />
<center><math>p_m=\frac{1}{ap+(1-a)}*p</math></center><br />
<center> where <math>a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}</math> and <math>a≤0</math></center><br />
<br />
<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Therefore, regardless of the margin function (<math>f</math>), the minimization of the softmax probability will ensure success.<br />
<br />
Compared to AM-LFS, this method involves only one parameter (<math>a</math>) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (<math>p_m={a_i}p+b_i</math>) may not be discriminative because it could be larger than the softmax probability.<br />
<br />
=== Random Search ===<br />
Unified formulation <math>L_5</math> is generated by inserting a simple modulating function <math>h{(a,p)}=\frac{1}{ap+(1-a)}</math> into the original softmax loss. It can be written as below [1]:<br />
<br />
<center><math>L_5=-log{(h{(a,p)}*p)}</math> where <math>h \in (0,1]</math> and <math>a≤0</math></center><br />
<br />
In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br />
<br />
=== Reward-Guided Search ===<br />
Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward [3]. The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br />
<br />
<center><math>G_t \overset{\Delta}{=} R_t+R_t+1+R_t+2+⋯+R_T</math></center><br />
<br />
where <math>G_t</math> = cumulative reward, <math>R_t</math> = immediate reward, and <math>R_T</math> = end of episode.<br />
<br />
<math>G_t</math> is the sum of immediate rewards from arbitrary time <math>t</math>. <math>G_t</math> is a random variable because it depends on immediate reward which depends on the agent action and the environment reaction to this action.<br />
<br />
=== Optimization ===<br />
<br />
== Results and Discussion ==<br />
=== Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br />
<br />
<br />
=== Results on RFW ===<br />
<br />
<br />
=== Results on MegaFace and Trillion-Pairs ===<br />
<br />
<br />
== Conclusion ==<br />
In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. <br />
<br />
<br />
== Critiques ==<br />
- Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument.<br />
- Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would.<br />
- AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate.<br />
- The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show much advantage since they produce very similar results. More complicated data set needs to be tested to prove the method's reliability.<br />
<br />
<br />
== References ==<br />
[1] X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, "Loss Function Search for Face Recognition", in International Conference on Machine Learning, 2020, pp. 1-10.<br />
<br />
[2] Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br />
2020].<br />
<br />
[3] S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br />
<br />
[4] “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br />
<br />
[5] B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div>Jcllau