http://wiki.math.uwaterloo.ca/statwiki/api.php?action=feedcontributions&user=Mhamdy&feedformat=atomstatwiki - User contributions [US]2022-12-03T15:30:15ZUser contributionsMediaWiki 1.28.3http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Neural_ODEs&diff=46194Neural ODEs2020-11-24T04:27:34Z<p>Mhamdy: /* A Generative Latent Function Time-Series Model */</p>
<hr />
<div>== Introduction ==<br />
Chen et al. propose a new class of neural networks called neural ordinary differential equations (ODEs) in their 2018 paper under the same title. Neural network models, such as residual or recurrent networks, can be generalized as a set of transformations through hidden states (a.k.a layers) <math>\mathbf{h}</math>, given by the equation <br />
<br />
<div style="text-align:center;"><math> \mathbf{h}_{t+1} = \mathbf{h}_t + f(\mathbf{h}_t,\theta_t) </math> (1) </div><br />
<br />
where <math>t \in \{0,...,T\}</math> and <math>\theta_t</math> corresponds to the set of parameters or weights in state <math>t</math>. It is important to note that it has been shown (Lu et al., 2017)(Haber<br />
and Ruthotto, 2017)(Ruthotto and Haber, 2018) that Equation 1 can be viewed as an Euler discretization. Given this Euler description, if the number of layers and step size between layers are taken to their limits, then Equation 1 can instead be described continuously in the form of the ODE, <br />
<br />
<div style="text-align:center;"><math> \frac{d\mathbf{h}(t)}{dt} = f(\mathbf{h}(t),t,\theta) </math> (2). </div><br />
<br />
Equation 2 now describes a network where the output layer <math>\mathbf{h}(T)</math> is generated by solving for the ODE at time <math>T</math>, given the initial value at <math>t=0</math>, where <math>\mathbf{h}(0)</math> is the input layer of the network. <br />
<br />
With a vast amount of theory and research in the field of solving ODEs numerically, there are a number of benefits to formulating the hidden state dynamics this way. One major advantage is that a continuous description of the network allows for the calculation of <math>f</math> at arbitrary intervals and locations. The authors provide an example in section five of how the neural ODE network outperforms the discretized version i.e. residual networks, by taking advantage of the continuity of <math>f</math>. A depiction of this distinction is shown in the figure below. <br />
<br />
<div style="text-align:center;"> [[File:NeuralODEs_Fig1.png|350px]] </div><br />
<br />
In section four the authors show that the single-unit bottleneck of normalizing flows can be overcome by constructing a new class of density models that incorporates the neural ODE network formulation.<br />
The next section on automatic differentiation will describe how utilizing ODE solvers allows for the calculation of gradients of the loss function without storing any of the hidden state information. This results in a very low memory requirement for neural ODE networks in comparison to traditional networks that rely on intermediate hidden state quantities for backpropagation.<br />
<br />
== Reverse-mode Automatic Differentiation of ODE Solutions ==<br />
Like most neural networks, optimizing the weight parameters <math>\theta</math> for a neural ODE network involves finding the gradient of a loss function with respect to those parameters. Differentiating in the forward direction is a simple task, however, this method is very computationally expensive and unstable, as it introduces additional numerical error. Instead, the authors suggest that the gradients can be calculated in the reverse-mode with the adjoint sensitivity method (Pontryagin et al., 1962). This "backpropagation" method solves an augmented version of the forward ODE problem but in reverse, which is something that all ODE solvers are capable of. Section 3 provides results showing that this method gives very desirable memory costs and numerical stability. <br />
<br />
The authors provide an example of the adjoint method by considering the minimization of the scalar-valued loss function <math>L</math>, which takes the solution of the ODE solver as its argument.<br />
<br />
<div style="text-align:center;">[[File:NeuralODEs_Eq1.png|700px]],</div> <br />
This minimization problem requires the calculation of <math>\frac{\partial L}{\partial \mathbf{z}(t_0)}</math> and <math>\frac{\partial L}{\partial \theta}</math>.<br />
<br />
The adjoint itself is defined as <math>\mathbf{a}(t) = \frac{\partial L}{\partial \mathbf{z}(t)}</math>, which describes the gradient of the loss with respect to the hidden state <math>\mathbf{z}(t)</math>. By taking the first derivative of the adjoint, another ODE arises in the form of,<br />
<br />
<div style="text-align:center;"><math>\frac{d \mathbf{a}(t)}{dt} = -\mathbf{a}(t)^T \frac{\partial f(\mathbf{z}(t),t,\theta)}{\partial \mathbf{z}}</math> (3).</div> <br />
<br />
Since the value <math>\mathbf{a}(t_0)</math> is required to minimize the loss, the ODE in equation 3 must be solved backwards in time from <math>\mathbf{a}(t_1)</math>. Solving this problem is dependent on the knowledge of the hidden state <math>\mathbf{z}(t)</math> for all <math>t</math>, which an neural ODE does not save on the forward pass. Luckily, both <math>\mathbf{a}(t)</math> and <math>\mathbf{z}(t)</math> can be calculated in reverse, at the same time, by setting up an augmented version of the dynamics and is shown in the final algorithm. Finally, the derivative <math>dL/d\theta</math> can be expressed in terms of the adjoint and the hidden state as, <br />
<br />
<div style="text-align:center;"><math> \frac{dL}{d\theta} -\int_{t_1}^{t_0} \mathbf{a}(t)^T\frac{\partial f(\mathbf{z}(t),t,\theta)}{\partial \theta}dt</math> (4).</div><br />
<br />
To obtain very inexpensive calculations of <math>\frac{\partial f}{\partial z}</math> and <math>\frac{\partial f}{\partial \theta}</math> in equation 3 and 4, automatic differentiation can be utilized. The authors present an algorithm to calculate the gradients of <math>L</math> and their dependent quantities with only one call to an ODE solver and is shown below. <br />
<br />
<div style="text-align:center;">[[File:NeuralODEs Algorithm1.png|850px]]</div><br />
<br />
If the loss function has a stronger dependence on the hidden states for <math>t \neq t_0,t_1</math>, then Algorithm 1 can be modified to handle multiple calls to the ODESolve step since most ODE solvers have the capability to provide <math>z(t)</math> at arbitrary times. A visual depiction of this scenario is shown below. <br />
<br />
<div style="text-align:center;">[[File:NeuralODES Fig2.png|350px]]</div><br />
<br />
Please see the [https://arxiv.org/pdf/1806.07366.pdf#page=13 appendix] for extended versions of Algorithm 1 and detailed derivations of each equation in this section.<br />
<br />
== Replacing Residual Networks with ODEs for Supervised Learning ==<br />
Section three of the paper investigates an application of the reverse-mode differentiation described in section two, for the training of neural ODE networks on the MNIST digit data set. To solve for the forward pass in the neural ODE network, the following experiment used Adams method, which is an implicit ODE solver. Although it has a marked improvement over explicit ODE solvers in numerical accuracy, integrating backward through the network for backpropagation is still not preferred and the adjoint sensitivity method is used to perform efficient weight optimization. The network with this "backpropagation" technique is referred to as ODE-Net in this section. <br />
<br />
=== Implementation ===<br />
A residual network (ResNet), studied by He et al. (2016), with six standard residual blocks was used as a comparative model for this experiment. The competing model, ODE-net, replaces the residual blocks of the ResNet with the Adams solver. As a hybrid of the two models ResNet and ODE-net, a third network was created called RK-Net, which solves the weight optimization of the neural ODE network explicitly through backward Runge-Kutta integration. The following table shows the training and performance results of each network. <br />
<br />
<div style="text-align:center;">[[File:NeuralODEs Table1.png|400px]]</div><br />
<br />
Note that <math>L</math> and <math>\tilde{L}</math> are the number of layers in ResNet and the number of function calls that the Adams method makes for the two ODE networks and are effectively analogous quantities. As shown in Table 1, both of the ODE networks achieve comparable performance to that of the ResNet with a notable decrease in memory cost for ODE-net.<br />
<br />
<br />
Another interesting component of ODE networks is the ability to control the tolerance in the ODE solver used and subsequently the numerical error in the solution. <br />
<br />
<div style="text-align:center;">[[File:NeuralODEs Fig3.png|700px]]</div><br />
<br />
The tolerance of the ODE solver is represented by the colour bar in Figure 3 above and notice that a variety of effects arise from adjusting this parameter. Primarily, if one was to treat the tolerance as a hyperparameter of sorts, you could tune it such that you find a balance between accuracy (Figure 3a) and computational complexity (Figure 3b). Figure 3c also provides further evidence for the benefits of the adjoint method for the backward pass in ODE-nets since there is a nearly 1:0.5 ratio of forward to backward function calls. In the ResNet and RK-Net examples, this ratio is 1:1.<br />
<br />
Additionally, the authors loosely define the concept of depth in a neural ODE network by referring to Figure 3d. Here it's evident that as you continue to train an ODE network, the number of function evaluations the ODE solver performs increases. As previously mentioned, this quantity is comparable to the network depth of a discretized network. However, as the authors note, this result should be seen as the progression of the network's complexity over training epochs, which is something we expect to increase over time.<br />
<br />
== Continuous Normalizing Flows ==<br />
<br />
Section four tackles the implementation of continuous-depth Neural Networks, but to do so, in the first part of section four the authors discuss theoretically how to establish this kind of network through the use of normalizing flows. The authors use a change of variables method presented in other works (Rezende and Mohamed, 2015), (Dinh et al., 2014), to compute the change of a probability distribution if sample points are transformed through a bijective function, <math>f</math>.<br />
<br />
<div style="text-align:center;"><math>z_1=f(z_0) \Rightarrow \log(p(z_1))=\log(p(z_0))-\log|\det\frac{\partial f}{\partial z_0}|</math></div><br />
<br />
Where p(z) is the probability distribution of the samples and <math>det\frac{\partial f}{\partial z_0}</math> is the determinant of the Jacobian which has a cubic cost in the dimension of '''z''' or the number of hidden units in the network. The authors discovered however that transforming the discrete set of hidden layers in the normalizing flow network to continuous transformations simplifies the computations significantly, due primarily to the following theorem:<br />
<br />
'''''Theorem 1:''' (Instantaneous Change of Variables). Let z(t) be a finite continuous random variable with probability p(z(t)) dependent on time. Let dz/dt=f(z(t),t) be a differential equation describing a continuous-in-time transformation of z(t). Assuming that f is uniformly Lipschitz continuous in z and continuous in t, then the change in log probability also follows a differential equation:''<br />
<br />
<div style="text-align:center;"><math>\frac{\partial \log(p(z(t)))}{\partial t}=-tr\left(\frac{df}{dz(t)}\right)</math></div><br />
<br />
The biggest advantage to using this theorem is that the trace function is a linear function, so if the dynamics of the problem, f, is represented by a sum of functions, then so is the log density. This essentially means that you can now compute flow models with only a linear cost with respect to the number of hidden units, <math>M</math>. In standard normalizing flow models, the cost is <math>O(M^3)</math>, so they will generally fit many layers with a single hidden unit in each layer.<br />
<br />
Finally the authors use these realizations to construct Continuous Normalizing Flow networks (CNFs) by specifying the parameters of the flow as a function of ''t'', ie, <math>f(z(t),t)</math>. They also use a gating mechanism for each hidden unit, <math>\frac{dz}{dt}=\sum_n \sigma_n(t)f_n(z)</math> where <math>\sigma_n(t)\in (0,1)</math> is a separate neural network which learns when to apply each dynamic <math>f_n</math>.<br />
<br />
===Implementation===<br />
<br />
The authors construct two separate types of neural networks to compare against each other, the first is the standard planar Normalizing Flow network (NF) using 64 layers of single hidden units, and the second is their new CNF with 64 hidden units. The NF model is trained over 500,000 iterations using RMSprop, and the CNF network is trained over 10,000 iterations using Adam. The loss function is <math>KL(q(x)||p(x))</math> where <math>q(x)</math> is the flow model and <math>p(x)</math> is the target probability density.<br />
<br />
One of the biggest advantages when implementing CNF is that you can train the flow parameters just by performing maximum likelihood estimation on <math>\log(q(x))</math> given <math>p(x)</math>, where <math>q(x)</math> is found via the theorem above, and then reversing the CNF to generate random samples from <math>q(x)</math>. This reversal of the CNF is done with about the same cost of the forward pass which is not able to be done in an NF network. The following two figures demonstrate the ability of CNF to generate more expressive and accurate output data as compared to standard NF networks.<br />
<br />
<div style="text-align:center;"><br />
[[Image:CNFcomparisons.png]]<br />
<br />
[[Image:CNFtransitions.png]]<br />
</div><br />
<br />
Figure 4 shows clearly that the CNF structure exhibits significantly lower loss functions than NF. In figure 5 both networks were tasked with transforming a standard Gaussian distribution into a target distribution, not only was the CNF network more accurate on the two moons target, but also the steps it took along the way are much more intuitive than the output from NF.<br />
<br />
== A Generative Latent Function Time-Series Model ==<br />
<br />
One of the largest issues at play in terms of Neural ODE networks is the fact that in many instances, data points are either very sparsely distributed, or irregularly-sampled. The latent dynamics are discretized and the observations are in the bins of fixed duration. An example of this is medical records which are only updated when a patient visits a doctor or the hospital. To solve this issue the authors had to create a generative time-series model which would be able to fill in the gaps of missing data. The authors consider each time series as a latent trajectory stemming from the initial local state <math>z_{t_0 }</math> and determined from a global set of latent parameters. Given a set of observation times and initial state, the generative model constructs points via the following sample procedure:<br />
<br />
<div style="text-align:center;"><br />
<math><br />
z_{t_0}∼p(z_{t_0}) <br />
</math><br />
</div> <br />
<br />
<div style="text-align:center;"><br />
<math><br />
z_{t_1},z_{t_2},\dots,z_{t_N}={\rm ODESolve}(z_{t_0},f,θ_f,t_0,...,t_N)<br />
</math><br />
</div><br />
<br />
<div style="text-align:center;"><br />
each <br />
<math><br />
x_{t_i}∼p(x│z_{t_i},θ_x)<br />
</math><br />
</div><br />
<br />
<math>f</math> is a function which outputs the gradient <math>\frac{\partial z(t)}{\partial t}=f(z(t),θ_f)</math> which is parameterized via a neural net. In order to train this latent variable model, the authors had to first encode their given data and observation times using an RNN encoder, construct the new points using the trained parameters, then decode the points back into the original space. The following figure describes this process:<br />
<br />
<div style="text-align:center;"><br />
[[Image:EncodingFigure.png]]<br />
</div><br />
<br />
Another variable which could affect the latent state of a time-series model is how often an event actually occurs. The authors solved this by parameterizing the rate of events in terms of a Poisson process. They described the set of independent observation times in an interval <math>\left[t_{start},t_{end}\right]</math> as:<br />
<br />
<div style="text-align:center;"> <br />
<math><br />
{\rm log}(p(t_1,t_2,\dots,t_N ))=\sum_{i=1}^N{\rm log}(\lambda(z(t_i)))-\int_{t_{start}}^{t_{end}}λ(z(t))dt<br />
</math><br />
</div><br />
<br />
where <math>\lambda(*)</math> is parameterized via another neural network.<br />
<br />
===Implementation===<br />
<br />
To test the effectiveness of the Latent time-series ODE model (LODE), they fit the encoder with 25 hidden units, parametrize function f with a one-layer 20 hidden unit network, and the decoder as another neural network with 20 hidden units. They compare this against a standard recurrent neural net (RNN) with 25 hidden units trained to minimize gaussian log-likelihood. The authors tested both of these network systems on a dataset of 2-dimensional spirals which either rotated clockwise or counter-clockwise and sampled the positions of each spiral at 100 equally spaced time steps. They can then simulate irregularly timed data by taking random amounts of points without replacement from each spiral. The next two figures show the outcome of these experiments:<br />
<br />
<div style="text-align:center;"><br />
[[Image:LODEtestresults.png]] [[Image:SpiralFigure.png|The blue lines represent the test data learned curves and the red lines represent the extrapolated curves predicted by each model]]<br />
</div><br />
<br />
In the figure on the right the blue lines represent the test data learned curves and the red lines represent the extrapolated curves predicted by each model. It is noted that the LODE performs significantly better than the standard RNN model, especially on smaller sets of data points.<br />
<br />
== Scope and Limitations ==<br />
<br />
Section 6 mainly discusses the scope and limitations of the paper. Firstly while “batching” the training data is a useful step in standard neural nets, and can still be applied here by combining the ODEs associated with each batch, the authors found that controlling the error, in this case, may increase the number of calculations required. In practice, however, the number of calculations did not increase significantly.<br />
<br />
So long as the model proposed in this paper uses finite weights and Lipschitz nonlinearities, then Picard’s existence theorem (Coddington and Levinson, 1955) applies, guaranteeing the solution to the IVP exists and is unique. This theorem holds for the model presented above when the network has finite weights and uses nonlinearities in the Lipshitz class. <br />
<br />
In controlling the amount of error in the model, the authors were only able to reduce tolerances to approximately <math>10^{-3}</math> and <math>10^{-5}</math> in classification and density estimation respectively without also degrading the computational performance.<br />
<br />
The authors believe that reconstructing state trajectories by running the dynamics backward can introduce extra numerical error. They address a possible solution to this problem by checkpointing certain time steps and storing intermediate values of z on the forward pass. Then while reconstructing, you do each part individually between checkpoints. The authors acknowledged that they informally checked the validity of this method since they don’t consider it a practical problem.<br />
<br />
There remain, however, areas where standard neural networks may perform better than Neural ODEs. Firstly, conventional nets can fit non-homeomorphic functions, for example, functions whose output has a smaller dimension that their input, or that change the topology of the input space. However, this could be handled by composing ODE nets with standard network layers. Another point is that conventional nets can be evaluated exactly with a fixed amount of computation, and are typically faster to train and do not require an error tolerance for a solver.<br />
<br />
== Conclusions and Critiques ==<br />
<br />
We covered the use of black-box ODE solvers as a model component and their application to initial value problems constructed from real applications. Neural ODE Networks show promising gains in computational cost without large sacrifices in accuracy when applied to certain problems. A drawback of some of these implementations is that the ODE Neural Networks are limited by the underlying distributions of the problems they are trying to solve (requirement of Lipschitz continuity, etc.). There are plenty of further advances to be made in this field as hundreds of years of ODE theory and literature is available, so this is currently an important area of research.<br />
<br />
ODEs indeed represent an important area of applied mathematics where neural networks can be used to solve them numerically. Perhaps, a parallel area of investigation can be PDEs (Partial Differential Equations). PDEs are also widely encountered in many areas of applied mathematics, physics, social sciences and many other fields. It will be interesting to see how neural networks can be used to solve PDEs.<br />
<br />
== More Critiques ==<br />
<br />
This paper covers the memory efficiency of Neural ODE Networks, but does not address runtime. In practice, most systems are bound by latency requirements more-so than memory requirements (except in edge device cases). Though it may be unreasonable to expect the authors to produce a performance-optimized implementation, it would be insightful to understand the computational bottlenecks so existing frameworks can take steps to address them. This model looks promising and practical performance is the key to enabling future research in this.<br />
<br />
The above critique also questions the need for a neural network for such a problem. This problem was studied by Brunel et al. and they presented their solution in their paper ''Parametric Estimation of Ordinary Differential Equations with Orthogonality Conditions''. While this solution also requires iteratively solving a complex optimization problem, they did not require the massive memory and runtime overhead of a neural network. For the neural network solution to demonstrate its potential, it should be including experimental comparisons with specialized ordinary differential equation algorithms instead of simply comparing with a general recurrent neural network.<br />
<br />
== References ==<br />
Yiping Lu, Aoxiao Zhong, Quanzheng Li, and Bin Dong. Beyond finite layer neural networks: Bridging deep architectures and numerical differential equations. ''arXiv preprint arXiv'':1710.10121, 2017.<br />
<br />
Eldad Haber and Lars Ruthotto. Stable architectures for deep neural networks. ''Inverse Problems'', 34 (1):014004, 2017.<br />
<br />
Lars Ruthotto and Eldad Haber. Deep neural networks motivated by partial differential equations. ''arXiv preprint arXiv'':1804.04272, 2018.<br />
<br />
Lev Semenovich Pontryagin, EF Mishchenko, VG Boltyanskii, and RV Gamkrelidze. ''The mathematical theory of optimal processes''. 1962.<br />
<br />
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Identity mappings in deep residual networks. In ''European conference on computer vision'', pages 630–645. Springer, 2016b.<br />
<br />
Earl A Coddington and Norman Levinson. ''Theory of ordinary differential equations''. Tata McGrawHill Education, 1955.<br />
<br />
Danilo Jimenez Rezende and Shakir Mohamed. Variational inference with normalizing flows. ''arXiv preprint arXiv:1505.05770'', 2015.<br />
<br />
Laurent Dinh, David Krueger, and Yoshua Bengio. NICE: Non-linear independent components estimation. ''arXiv preprint arXiv:1410.8516'', 2014.<br />
<br />
Brunel, N. J., Clairon, Q., & d’Alché-Buc, F. (2014). Parametric estimation of ordinary differential equations with orthogonality conditions. ''Journal of the American Statistical Association'', 109(505), 173-185.</div>Mhamdyhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Neural_ODEs&diff=46193Neural ODEs2020-11-24T04:26:46Z<p>Mhamdy: /* A Generative Latent Function Time-Series Model */</p>
<hr />
<div>== Introduction ==<br />
Chen et al. propose a new class of neural networks called neural ordinary differential equations (ODEs) in their 2018 paper under the same title. Neural network models, such as residual or recurrent networks, can be generalized as a set of transformations through hidden states (a.k.a layers) <math>\mathbf{h}</math>, given by the equation <br />
<br />
<div style="text-align:center;"><math> \mathbf{h}_{t+1} = \mathbf{h}_t + f(\mathbf{h}_t,\theta_t) </math> (1) </div><br />
<br />
where <math>t \in \{0,...,T\}</math> and <math>\theta_t</math> corresponds to the set of parameters or weights in state <math>t</math>. It is important to note that it has been shown (Lu et al., 2017)(Haber<br />
and Ruthotto, 2017)(Ruthotto and Haber, 2018) that Equation 1 can be viewed as an Euler discretization. Given this Euler description, if the number of layers and step size between layers are taken to their limits, then Equation 1 can instead be described continuously in the form of the ODE, <br />
<br />
<div style="text-align:center;"><math> \frac{d\mathbf{h}(t)}{dt} = f(\mathbf{h}(t),t,\theta) </math> (2). </div><br />
<br />
Equation 2 now describes a network where the output layer <math>\mathbf{h}(T)</math> is generated by solving for the ODE at time <math>T</math>, given the initial value at <math>t=0</math>, where <math>\mathbf{h}(0)</math> is the input layer of the network. <br />
<br />
With a vast amount of theory and research in the field of solving ODEs numerically, there are a number of benefits to formulating the hidden state dynamics this way. One major advantage is that a continuous description of the network allows for the calculation of <math>f</math> at arbitrary intervals and locations. The authors provide an example in section five of how the neural ODE network outperforms the discretized version i.e. residual networks, by taking advantage of the continuity of <math>f</math>. A depiction of this distinction is shown in the figure below. <br />
<br />
<div style="text-align:center;"> [[File:NeuralODEs_Fig1.png|350px]] </div><br />
<br />
In section four the authors show that the single-unit bottleneck of normalizing flows can be overcome by constructing a new class of density models that incorporates the neural ODE network formulation.<br />
The next section on automatic differentiation will describe how utilizing ODE solvers allows for the calculation of gradients of the loss function without storing any of the hidden state information. This results in a very low memory requirement for neural ODE networks in comparison to traditional networks that rely on intermediate hidden state quantities for backpropagation.<br />
<br />
== Reverse-mode Automatic Differentiation of ODE Solutions ==<br />
Like most neural networks, optimizing the weight parameters <math>\theta</math> for a neural ODE network involves finding the gradient of a loss function with respect to those parameters. Differentiating in the forward direction is a simple task, however, this method is very computationally expensive and unstable, as it introduces additional numerical error. Instead, the authors suggest that the gradients can be calculated in the reverse-mode with the adjoint sensitivity method (Pontryagin et al., 1962). This "backpropagation" method solves an augmented version of the forward ODE problem but in reverse, which is something that all ODE solvers are capable of. Section 3 provides results showing that this method gives very desirable memory costs and numerical stability. <br />
<br />
The authors provide an example of the adjoint method by considering the minimization of the scalar-valued loss function <math>L</math>, which takes the solution of the ODE solver as its argument.<br />
<br />
<div style="text-align:center;">[[File:NeuralODEs_Eq1.png|700px]],</div> <br />
This minimization problem requires the calculation of <math>\frac{\partial L}{\partial \mathbf{z}(t_0)}</math> and <math>\frac{\partial L}{\partial \theta}</math>.<br />
<br />
The adjoint itself is defined as <math>\mathbf{a}(t) = \frac{\partial L}{\partial \mathbf{z}(t)}</math>, which describes the gradient of the loss with respect to the hidden state <math>\mathbf{z}(t)</math>. By taking the first derivative of the adjoint, another ODE arises in the form of,<br />
<br />
<div style="text-align:center;"><math>\frac{d \mathbf{a}(t)}{dt} = -\mathbf{a}(t)^T \frac{\partial f(\mathbf{z}(t),t,\theta)}{\partial \mathbf{z}}</math> (3).</div> <br />
<br />
Since the value <math>\mathbf{a}(t_0)</math> is required to minimize the loss, the ODE in equation 3 must be solved backwards in time from <math>\mathbf{a}(t_1)</math>. Solving this problem is dependent on the knowledge of the hidden state <math>\mathbf{z}(t)</math> for all <math>t</math>, which an neural ODE does not save on the forward pass. Luckily, both <math>\mathbf{a}(t)</math> and <math>\mathbf{z}(t)</math> can be calculated in reverse, at the same time, by setting up an augmented version of the dynamics and is shown in the final algorithm. Finally, the derivative <math>dL/d\theta</math> can be expressed in terms of the adjoint and the hidden state as, <br />
<br />
<div style="text-align:center;"><math> \frac{dL}{d\theta} -\int_{t_1}^{t_0} \mathbf{a}(t)^T\frac{\partial f(\mathbf{z}(t),t,\theta)}{\partial \theta}dt</math> (4).</div><br />
<br />
To obtain very inexpensive calculations of <math>\frac{\partial f}{\partial z}</math> and <math>\frac{\partial f}{\partial \theta}</math> in equation 3 and 4, automatic differentiation can be utilized. The authors present an algorithm to calculate the gradients of <math>L</math> and their dependent quantities with only one call to an ODE solver and is shown below. <br />
<br />
<div style="text-align:center;">[[File:NeuralODEs Algorithm1.png|850px]]</div><br />
<br />
If the loss function has a stronger dependence on the hidden states for <math>t \neq t_0,t_1</math>, then Algorithm 1 can be modified to handle multiple calls to the ODESolve step since most ODE solvers have the capability to provide <math>z(t)</math> at arbitrary times. A visual depiction of this scenario is shown below. <br />
<br />
<div style="text-align:center;">[[File:NeuralODES Fig2.png|350px]]</div><br />
<br />
Please see the [https://arxiv.org/pdf/1806.07366.pdf#page=13 appendix] for extended versions of Algorithm 1 and detailed derivations of each equation in this section.<br />
<br />
== Replacing Residual Networks with ODEs for Supervised Learning ==<br />
Section three of the paper investigates an application of the reverse-mode differentiation described in section two, for the training of neural ODE networks on the MNIST digit data set. To solve for the forward pass in the neural ODE network, the following experiment used Adams method, which is an implicit ODE solver. Although it has a marked improvement over explicit ODE solvers in numerical accuracy, integrating backward through the network for backpropagation is still not preferred and the adjoint sensitivity method is used to perform efficient weight optimization. The network with this "backpropagation" technique is referred to as ODE-Net in this section. <br />
<br />
=== Implementation ===<br />
A residual network (ResNet), studied by He et al. (2016), with six standard residual blocks was used as a comparative model for this experiment. The competing model, ODE-net, replaces the residual blocks of the ResNet with the Adams solver. As a hybrid of the two models ResNet and ODE-net, a third network was created called RK-Net, which solves the weight optimization of the neural ODE network explicitly through backward Runge-Kutta integration. The following table shows the training and performance results of each network. <br />
<br />
<div style="text-align:center;">[[File:NeuralODEs Table1.png|400px]]</div><br />
<br />
Note that <math>L</math> and <math>\tilde{L}</math> are the number of layers in ResNet and the number of function calls that the Adams method makes for the two ODE networks and are effectively analogous quantities. As shown in Table 1, both of the ODE networks achieve comparable performance to that of the ResNet with a notable decrease in memory cost for ODE-net.<br />
<br />
<br />
Another interesting component of ODE networks is the ability to control the tolerance in the ODE solver used and subsequently the numerical error in the solution. <br />
<br />
<div style="text-align:center;">[[File:NeuralODEs Fig3.png|700px]]</div><br />
<br />
The tolerance of the ODE solver is represented by the colour bar in Figure 3 above and notice that a variety of effects arise from adjusting this parameter. Primarily, if one was to treat the tolerance as a hyperparameter of sorts, you could tune it such that you find a balance between accuracy (Figure 3a) and computational complexity (Figure 3b). Figure 3c also provides further evidence for the benefits of the adjoint method for the backward pass in ODE-nets since there is a nearly 1:0.5 ratio of forward to backward function calls. In the ResNet and RK-Net examples, this ratio is 1:1.<br />
<br />
Additionally, the authors loosely define the concept of depth in a neural ODE network by referring to Figure 3d. Here it's evident that as you continue to train an ODE network, the number of function evaluations the ODE solver performs increases. As previously mentioned, this quantity is comparable to the network depth of a discretized network. However, as the authors note, this result should be seen as the progression of the network's complexity over training epochs, which is something we expect to increase over time.<br />
<br />
== Continuous Normalizing Flows ==<br />
<br />
Section four tackles the implementation of continuous-depth Neural Networks, but to do so, in the first part of section four the authors discuss theoretically how to establish this kind of network through the use of normalizing flows. The authors use a change of variables method presented in other works (Rezende and Mohamed, 2015), (Dinh et al., 2014), to compute the change of a probability distribution if sample points are transformed through a bijective function, <math>f</math>.<br />
<br />
<div style="text-align:center;"><math>z_1=f(z_0) \Rightarrow \log(p(z_1))=\log(p(z_0))-\log|\det\frac{\partial f}{\partial z_0}|</math></div><br />
<br />
Where p(z) is the probability distribution of the samples and <math>det\frac{\partial f}{\partial z_0}</math> is the determinant of the Jacobian which has a cubic cost in the dimension of '''z''' or the number of hidden units in the network. The authors discovered however that transforming the discrete set of hidden layers in the normalizing flow network to continuous transformations simplifies the computations significantly, due primarily to the following theorem:<br />
<br />
'''''Theorem 1:''' (Instantaneous Change of Variables). Let z(t) be a finite continuous random variable with probability p(z(t)) dependent on time. Let dz/dt=f(z(t),t) be a differential equation describing a continuous-in-time transformation of z(t). Assuming that f is uniformly Lipschitz continuous in z and continuous in t, then the change in log probability also follows a differential equation:''<br />
<br />
<div style="text-align:center;"><math>\frac{\partial \log(p(z(t)))}{\partial t}=-tr\left(\frac{df}{dz(t)}\right)</math></div><br />
<br />
The biggest advantage to using this theorem is that the trace function is a linear function, so if the dynamics of the problem, f, is represented by a sum of functions, then so is the log density. This essentially means that you can now compute flow models with only a linear cost with respect to the number of hidden units, <math>M</math>. In standard normalizing flow models, the cost is <math>O(M^3)</math>, so they will generally fit many layers with a single hidden unit in each layer.<br />
<br />
Finally the authors use these realizations to construct Continuous Normalizing Flow networks (CNFs) by specifying the parameters of the flow as a function of ''t'', ie, <math>f(z(t),t)</math>. They also use a gating mechanism for each hidden unit, <math>\frac{dz}{dt}=\sum_n \sigma_n(t)f_n(z)</math> where <math>\sigma_n(t)\in (0,1)</math> is a separate neural network which learns when to apply each dynamic <math>f_n</math>.<br />
<br />
===Implementation===<br />
<br />
The authors construct two separate types of neural networks to compare against each other, the first is the standard planar Normalizing Flow network (NF) using 64 layers of single hidden units, and the second is their new CNF with 64 hidden units. The NF model is trained over 500,000 iterations using RMSprop, and the CNF network is trained over 10,000 iterations using Adam. The loss function is <math>KL(q(x)||p(x))</math> where <math>q(x)</math> is the flow model and <math>p(x)</math> is the target probability density.<br />
<br />
One of the biggest advantages when implementing CNF is that you can train the flow parameters just by performing maximum likelihood estimation on <math>\log(q(x))</math> given <math>p(x)</math>, where <math>q(x)</math> is found via the theorem above, and then reversing the CNF to generate random samples from <math>q(x)</math>. This reversal of the CNF is done with about the same cost of the forward pass which is not able to be done in an NF network. The following two figures demonstrate the ability of CNF to generate more expressive and accurate output data as compared to standard NF networks.<br />
<br />
<div style="text-align:center;"><br />
[[Image:CNFcomparisons.png]]<br />
<br />
[[Image:CNFtransitions.png]]<br />
</div><br />
<br />
Figure 4 shows clearly that the CNF structure exhibits significantly lower loss functions than NF. In figure 5 both networks were tasked with transforming a standard Gaussian distribution into a target distribution, not only was the CNF network more accurate on the two moons target, but also the steps it took along the way are much more intuitive than the output from NF.<br />
<br />
== A Generative Latent Function Time-Series Model ==<br />
<br />
One of the largest issues at play in terms of Neural ODE networks is the fact that in many instances, data points are either very sparsely distributed, or irregularly-sampled. The latent dynamics are discretized and the observations are in the bins of fixed duration. An example of this is medical records which are only updated when a patient visits a doctor or the hospital. To solve this issue the authors had to create a generative time-series model which would be able to fill in the gaps of missing data. The authors consider each time series as a latent trajectory stemming from the initial local state <math>z_{t_0 }</math> and determined from a global set of latent parameters. Given a set of observation times and initial state, the generative model constructs points via the following sample procedure:<br />
<br />
<div style="text-align:center;"><br />
<math><br />
z_{t_0}∼p(z_{t_0}) <br />
</math><br />
</div> <br />
<br />
<div style="text-align:center;"><br />
<math><br />
z_{t_1},z_{t_2},\dots,z_{t_N}=ODESolve(z_{t_0},f,θ_f,t_0,...,t_N)<br />
</math><br />
</div><br />
<br />
<div style="text-align:center;"><br />
each <br />
<math><br />
x_{t_i}∼p(x│z_{t_i},θ_x)<br />
</math><br />
</div><br />
<br />
<math>f</math> is a function which outputs the gradient <math>\frac{\partial z(t)}{\partial t}=f(z(t),θ_f)</math> which is parameterized via a neural net. In order to train this latent variable model, the authors had to first encode their given data and observation times using an RNN encoder, construct the new points using the trained parameters, then decode the points back into the original space. The following figure describes this process:<br />
<br />
<div style="text-align:center;"><br />
[[Image:EncodingFigure.png]]<br />
</div><br />
<br />
Another variable which could affect the latent state of a time-series model is how often an event actually occurs. The authors solved this by parameterizing the rate of events in terms of a Poisson process. They described the set of independent observation times in an interval <math>\left[t_{start},t_{end}\right]</math> as:<br />
<br />
<div style="text-align:center;"> <br />
<math><br />
{\rm log}(p(t_1,t_2,\dots,t_N ))=\sum_{i=1}^N{\rm log}(\lambda(z(t_i)))-\int_{t_{start}}^{t_{end}}λ(z(t))dt<br />
</math><br />
</div><br />
<br />
where <math>\lambda(*)</math> is parameterized via another neural network.<br />
<br />
===Implementation===<br />
<br />
To test the effectiveness of the Latent time-series ODE model (LODE), they fit the encoder with 25 hidden units, parametrize function f with a one-layer 20 hidden unit network, and the decoder as another neural network with 20 hidden units. They compare this against a standard recurrent neural net (RNN) with 25 hidden units trained to minimize gaussian log-likelihood. The authors tested both of these network systems on a dataset of 2-dimensional spirals which either rotated clockwise or counter-clockwise and sampled the positions of each spiral at 100 equally spaced time steps. They can then simulate irregularly timed data by taking random amounts of points without replacement from each spiral. The next two figures show the outcome of these experiments:<br />
<br />
<div style="text-align:center;"><br />
[[Image:LODEtestresults.png]] [[Image:SpiralFigure.png|The blue lines represent the test data learned curves and the red lines represent the extrapolated curves predicted by each model]]<br />
</div><br />
<br />
In the figure on the right the blue lines represent the test data learned curves and the red lines represent the extrapolated curves predicted by each model. It is noted that the LODE performs significantly better than the standard RNN model, especially on smaller sets of data points.<br />
<br />
== Scope and Limitations ==<br />
<br />
Section 6 mainly discusses the scope and limitations of the paper. Firstly while “batching” the training data is a useful step in standard neural nets, and can still be applied here by combining the ODEs associated with each batch, the authors found that controlling the error, in this case, may increase the number of calculations required. In practice, however, the number of calculations did not increase significantly.<br />
<br />
So long as the model proposed in this paper uses finite weights and Lipschitz nonlinearities, then Picard’s existence theorem (Coddington and Levinson, 1955) applies, guaranteeing the solution to the IVP exists and is unique. This theorem holds for the model presented above when the network has finite weights and uses nonlinearities in the Lipshitz class. <br />
<br />
In controlling the amount of error in the model, the authors were only able to reduce tolerances to approximately <math>10^{-3}</math> and <math>10^{-5}</math> in classification and density estimation respectively without also degrading the computational performance.<br />
<br />
The authors believe that reconstructing state trajectories by running the dynamics backward can introduce extra numerical error. They address a possible solution to this problem by checkpointing certain time steps and storing intermediate values of z on the forward pass. Then while reconstructing, you do each part individually between checkpoints. The authors acknowledged that they informally checked the validity of this method since they don’t consider it a practical problem.<br />
<br />
There remain, however, areas where standard neural networks may perform better than Neural ODEs. Firstly, conventional nets can fit non-homeomorphic functions, for example, functions whose output has a smaller dimension that their input, or that change the topology of the input space. However, this could be handled by composing ODE nets with standard network layers. Another point is that conventional nets can be evaluated exactly with a fixed amount of computation, and are typically faster to train and do not require an error tolerance for a solver.<br />
<br />
== Conclusions and Critiques ==<br />
<br />
We covered the use of black-box ODE solvers as a model component and their application to initial value problems constructed from real applications. Neural ODE Networks show promising gains in computational cost without large sacrifices in accuracy when applied to certain problems. A drawback of some of these implementations is that the ODE Neural Networks are limited by the underlying distributions of the problems they are trying to solve (requirement of Lipschitz continuity, etc.). There are plenty of further advances to be made in this field as hundreds of years of ODE theory and literature is available, so this is currently an important area of research.<br />
<br />
ODEs indeed represent an important area of applied mathematics where neural networks can be used to solve them numerically. Perhaps, a parallel area of investigation can be PDEs (Partial Differential Equations). PDEs are also widely encountered in many areas of applied mathematics, physics, social sciences and many other fields. It will be interesting to see how neural networks can be used to solve PDEs.<br />
<br />
== More Critiques ==<br />
<br />
This paper covers the memory efficiency of Neural ODE Networks, but does not address runtime. In practice, most systems are bound by latency requirements more-so than memory requirements (except in edge device cases). Though it may be unreasonable to expect the authors to produce a performance-optimized implementation, it would be insightful to understand the computational bottlenecks so existing frameworks can take steps to address them. This model looks promising and practical performance is the key to enabling future research in this.<br />
<br />
The above critique also questions the need for a neural network for such a problem. This problem was studied by Brunel et al. and they presented their solution in their paper ''Parametric Estimation of Ordinary Differential Equations with Orthogonality Conditions''. While this solution also requires iteratively solving a complex optimization problem, they did not require the massive memory and runtime overhead of a neural network. For the neural network solution to demonstrate its potential, it should be including experimental comparisons with specialized ordinary differential equation algorithms instead of simply comparing with a general recurrent neural network.<br />
<br />
== References ==<br />
Yiping Lu, Aoxiao Zhong, Quanzheng Li, and Bin Dong. Beyond finite layer neural networks: Bridging deep architectures and numerical differential equations. ''arXiv preprint arXiv'':1710.10121, 2017.<br />
<br />
Eldad Haber and Lars Ruthotto. Stable architectures for deep neural networks. ''Inverse Problems'', 34 (1):014004, 2017.<br />
<br />
Lars Ruthotto and Eldad Haber. Deep neural networks motivated by partial differential equations. ''arXiv preprint arXiv'':1804.04272, 2018.<br />
<br />
Lev Semenovich Pontryagin, EF Mishchenko, VG Boltyanskii, and RV Gamkrelidze. ''The mathematical theory of optimal processes''. 1962.<br />
<br />
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Identity mappings in deep residual networks. In ''European conference on computer vision'', pages 630–645. Springer, 2016b.<br />
<br />
Earl A Coddington and Norman Levinson. ''Theory of ordinary differential equations''. Tata McGrawHill Education, 1955.<br />
<br />
Danilo Jimenez Rezende and Shakir Mohamed. Variational inference with normalizing flows. ''arXiv preprint arXiv:1505.05770'', 2015.<br />
<br />
Laurent Dinh, David Krueger, and Yoshua Bengio. NICE: Non-linear independent components estimation. ''arXiv preprint arXiv:1410.8516'', 2014.<br />
<br />
Brunel, N. J., Clairon, Q., & d’Alché-Buc, F. (2014). Parametric estimation of ordinary differential equations with orthogonality conditions. ''Journal of the American Statistical Association'', 109(505), 173-185.</div>Mhamdyhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Streaming_Bayesian_Inference_for_Crowdsourced_Classification&diff=46191Streaming Bayesian Inference for Crowdsourced Classification2020-11-24T03:40:15Z<p>Mhamdy: /* Dawid-Skene Model for Crowdsourcing */</p>
<hr />
<div>Group 4 Paper Presentation Summary<br />
<br />
By Jonathan Chow, Nyle Dharani, Ildar Nasirov<br />
<br />
== Motivation ==<br />
Crowdsourcing can be a useful tool for data generation in classification projects by collecting annotations of large groups. Typically, this takes the form of online questions which many respondents will manually answer for payment. One example of this is Amazon's Mechanical Turk, a website where businesses (or "requesters") will remotely hire individuals(known as "Turkers" or "crowdsourcers") to perform human intelligence tasks (tasks that computers cannot do). In theory, it is effective in processing high volumes of small tasks that would be expensive to achieve in other methods.<br />
<br />
The primary limitation of this method to acquire data is that respondents can submit incorrect responses so that we couldn't ensure the data quality.<br />
<br />
Therefore, the success of crowdsourcing is limited by how well ground-truth can be determined. The primary method for doing so is probabilistic inference. However, current methods are computationally expensive, lack theoretical guarantees, or are limited to specific settings. In the meantime, there are some approaches to focus on how we sample the data from the crowd, rather than how we aggregate it to improve the accuracy of the system.<br />
<br />
== Dawid-Skene Model for Crowdsourcing ==<br />
The one-coin Dawid-Skene model is popular for contextualizing crowdsourcing problems. For task <math>i</math> in set <math>M</math>, let the ground-truth be the binary <math>y_i = {\pm 1}</math>. We get labels <math>X = {x_{ij}}</math> where <math>j \in N</math> is the index for that worker.<br />
<br />
At each time step <math>t</math>, a worker <math>j = a(t) </math> provides their label for an assigned task <math>i</math> and provides the label <math>x_{ij} = {\pm 1}</math>. We denote responses up to time <math>t</math> via superscript.<br />
<br />
We let <math>x_{ij} = 0</math> if worker <math>j</math> has not completed task <math>i</math>. We assume that <math>P(x_{ij} = y_i) = p_j</math>. This implies that each worker is independent and has equal probability of correctly labelling regardless of task. In crowdsourcing the data, we must determine how workers are assigned to tasks. We introduce two methods.<br />
<br />
Under uniform sampling, workers are allocated to tasks such that each task is completed by the same number of workers, rounded to the nearest integer, and no worker completes a task more than once. This policy is given by <center><math>\pi_{uni}(t) = {\rm argmin}_{i \notin M_{a(t)}^t}\{ | N_i^t | \}.</math></center><br />
<br />
Under uncertainty sampling, we assign more workers to tasks that are less certain. Assuming, we are able to estimate the posterior probability of ground-truth, we can allocate workers to the task with the lowest probability of falling into the predicted class. This policy is given by <center><math>\pi_{us}(t) = {\rm argmin}_{i \notin M_{a(t)}^t}\{ (max_{k \in \{\pm 1\}} ( P(y_i = k | X^t) ) \}.</math></center><br />
<br />
We then need to aggregate the data. The simple method of majority voting makes predictions for a given task based on the class the most workers have assigned it, <math>\hat{y}_i = \text{sign}\{\sum_{j \in N_i} x_{ij}\}</math>.<br />
<br />
== Streaming Bayesian Inference for Crowdsourced Classification (SBIC) ==<br />
The aim of the SBIC algorithm is to estimate the posterior probability, <math>P(y, p | X^t, \theta)</math> where <math>X^t</math> are the observed responses at time <math>t</math> and <math>\theta</math> is our prior. We can then generate predictions <math>\hat{y}^t</math> as the marginal probability over each <math>y_i</math> given <math>X^t</math>, and <math>\theta</math>.<br />
<br />
We factor <math>P(y, p | X^t, \theta) \approx \prod_{i \in M} \mu_i^t (y_i) \prod_{j \in N} \nu_j^t (p_j) </math> where <math>\mu_i^t</math> corresponds to each task and <math>\nu_j^t</math> to each worker.<br />
<br />
We then sequentially optimize the factors <math>\mu^t</math> and <math>\nu^t</math>. We begin by assuming that the worker accuracy follows a beta distribution with parameters <math>\alpha</math> and <math>\beta</math>. Initialize the task factors <math>\mu_i^0(+1) = q</math> and <math>\mu_i^0(-1) = 1 – q</math> for all <math>i</math>.<br />
<br />
When a new label is observed at time <math>t</math>, we update the <math>\nu_j^t</math> of worker <math>j</math>. We then update <math>\mu_i</math>. These updates are given by<br />
<br />
<center><math>\nu_j^t(p_j) \sim \text{Beta}(\sum_{i \in M_j^{t - 1}} \mu_i^{t - 1}(x_{ij}) + \alpha, \sum_{i \in M_j^{t - 1}} \mu_i^{t - 1}(-x_{ij}) + \beta) </math></center><br />
<br />
<center><math>\mu_i^t(y_i) \propto \begin{cases} \mu_i^{t - 1}(y_i)\overline{p}_j^t & x_{ij} = y_i \\ \mu_i^{t - 1}(y_i)(1 - \overline{p}_j^t) & x_{ij} \ne y_i \end{cases}</math></center><br />
where <math>\hat{p}_j^t = \frac{\sum_{i \in M_j^{t - 1}} \mu_i^{t - 1}(x_{ij}) + \alpha}{|M_j^{t - 1}| + \alpha + \beta }</math>.<br />
<br />
We choose our predictions to be the maximum <math>\mu_i^t(k) </math> for <math>k= \{-1,1\}</math>.<br />
<br />
Depending on our ordering of labels <math>X</math>, we can select for different applications.<br />
<br />
== Fast SBIC ==<br />
The pseudocode for Fast SBIC is shown below.<br />
<br />
<center>[[Image:FastSBIC.png|800px|]]</center><br />
<br />
As the name implies, the goal of this algorithm is speed. To facilitate this, we leave the order of <math>X</math> unchanged.<br />
<br />
We express <math>\mu_i^t</math> in terms of its log-odds<br />
<center><math>z_i^t = \log(\frac{\mu_i^t(+1)}{ \mu_i^t(-1)}) = z_i^{t - 1} + x_{ij} \log(\frac{\overline{p}_j^t}{1 - \overline{p}_j^t })</math></center><br />
where <math>z_i^0 = \log(\frac{q}{1 - q})</math>.<br />
<br />
The product chain then becomes a summation and removes the need to normalize each <math>\mu_i^t</math>. We use these log-odds to compute worker accuracy,<br />
<br />
<center><math>\overline{p}_j^t = \frac{\sum_{i \in M_j^{t - 1}} \sigma(x_{ij} z_i^{t-1}) + \alpha}{|M_j^{t - 1}| + \alpha + \beta}</math></center><br />
where <math>\sigma(z_i^{t-1}) := \frac{1}{1 + exp(-z_i^{t - 1})} = \mu_i^{t - 1}(+1) </math><br />
<br />
The final predictions are made by choosing class <math>\hat{y}_i^T = \text{sign}(z_i^T) </math>. We see later that Fast SBIC has similar computational speed to majority voting.<br />
<br />
== Sorted SBIC ==<br />
To increase the accuracy of the SBIC algorithm in exchange for computational efficiency, we run the algorithm in parallel giving labels in different orders. The pseudocode for this algorithm is given below.<br />
<br />
<center>[[Image:SortedSBIC.png|800px|]]</center><br />
<br />
From the general discussion of SBIC, we know that predictions on task <math>i</math> are more accurate toward the end of the collection process. This is a result of observing more data points and having run more updates on <math>\mu_i^t</math> and <math>\nu_j^t</math> to move them further from their prior. This means that task <math>i</math> is predicted more accurately when its corresponding labels are seen closer to the end of the process.<br />
<br />
We take advantage of this property by maintaining a distinct “view” of the log-odds for each task. When a label is observed, we update views for all tasks except the one for which the label was observed. At the end of the collection process, we process skipped labels. When run online, this process must be repeated at every timestep.<br />
<br />
We see that sorted SBIC is slower than Fast SBIC by a factor of M, the number of tasks. However, we can reduce the complexity by viewing <math>s^k</math> across different tasks in an offline setting when the whole dataset is known in advance.<br />
<br />
== Theoretical Analysis ==<br />
The authors prove an exponential relationship between the error probability and the number of labels per task. This allows for an upper bound to be placed on the error, in the asymptotic regime, where it can be assumed the SBIC predictions are close to the true values. The two theorems, for the different sampling regimes, are presented below.<br />
<br />
<center>[[Image:Theorem1.png|800px|]]</center><br />
<br />
<center>[[Image:Theorem2.png|800px|]]</center><br />
<br />
== Empirical Analysis ==<br />
The purpose of the empirical analysis is to compare SBIC to the existing state of the art algorithms. The SBIC algorithm is run on five real-world binary classification datasets. The results can be found in the table below. Other algorithms in the comparison are, from left to right, majority voting, expectation-maximization, mean-field, belief-propagation, Monte-Carlo sampling, and triangular estimation. <br />
<br />
First of all, the algorithms are run on a synthetic data that meets the assumptions of an underlying one-coin Dawid-Skene model, which allows the authors to compare SBIC's performance empirically with the theoretical results previously shown. <br />
<br />
<center>[[Image:RealWorldResults.png|800px|]]</center><br />
<br />
In bold are the best performing algorithms for each dataset. We see that both versions of the SBIC algorithm are competitive, having similar prediction errors to EM, AMF, and MC. All are considered state-of-the-art Bayesian algorithms.<br />
<br />
The figure below shows the average time required to simulate predictions on synthetic data under an uncertainty sampling policy. We see that Fast SBIC is comparable to majority voting and significantly faster than the other algorithms. This speed improvement, coupled with comparable accuracy, makes the Fast SBIC algorithm powerful.<br />
<br />
<center>[[Image:TimeRequirement.png|800px|]]</center><br />
<br />
== Conclusion and Future Research ==<br />
In conclusion, we have seen that SBIC is computationally efficient, accurate in practice, and has theoretical guarantees. The authors intend to extend the algorithm to the multi-class case in the future.<br />
<br />
== Critique ==<br />
In crowdsourcing data, the cost associated with collecting additional labels is not usually prohibitively expensive. As a result, if there is concern over ground-truth, paying for additional data to ensure <math>X</math> is sufficiently dense may be the desired response as opposed to sacrificing ground-truth accuracy. This may result in the SBIC algorithm being less practically useful than intended.Perhaps, a study can be done to compare the cost of acquiring additional data and checking how much it improves the accuracy of ground-truth. This can help us decide the usefulness of this algorithm.Second, SBIC should be used in multiple types of data like audio, text and images to make sure that it delivers consistent results. <br />
<br />
The paper is tackling the classic problem of aggregating labels in a crowdsourced application, with a focus on speed. The algorithms proposed are fast and simple to implement and come with theoretical guarantees on the bounds for error rates. However, the paper starts with an objective of designing fast label aggregation algorithms for a streaming setting yet doesn’t spend any time motivating the applications in which such algorithms are needed. All the datasets used in the empirical analysis are static datasets therefore for the paper to be useful, the problem considered should be well motivated. It also appears that the output from the algorithm depends on the order in which the data is processed, which may need to be clarified. Finally, the theoretical results are presented under the assumption that the predictions of the FBI converge to the ground truth, however, the reasoning behind this assumption is not explained.<br />
<br />
The paper assumes that crowdsourcing from human beings is systematic: that is, respondents to the problems would act in similar ways that can be classified into some categories. There are lots of other factors that need to be considered for a human respondent, such as fatigue effects and conflicts of interest. Those factors would seriously jeopardize the validity of the results and the model if they were not carefully designed and taken care of. For example, one formally accurate subject reacts badly to the subject one day generating lots of faulty data, and it would take lots of correct votes to even out the effects. Even in lots of medical experiment that involves human subjects, with rigorous standards and procedures, the results could still be invalid. The trade-off for speed while sacrificing validity of results is not wise.<br />
<br />
== References ==<br />
[1] Manino, Tran-Thanh, and Jennings. Streaming Bayesian Inference for Crowdsourced Classification. 33rd Conference on Neural Information Processing Systems, 2019</div>Mhamdyhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Streaming_Bayesian_Inference_for_Crowdsourced_Classification&diff=46190Streaming Bayesian Inference for Crowdsourced Classification2020-11-24T03:39:37Z<p>Mhamdy: /* Dawid-Skene Model for Crowdsourcing */</p>
<hr />
<div>Group 4 Paper Presentation Summary<br />
<br />
By Jonathan Chow, Nyle Dharani, Ildar Nasirov<br />
<br />
== Motivation ==<br />
Crowdsourcing can be a useful tool for data generation in classification projects by collecting annotations of large groups. Typically, this takes the form of online questions which many respondents will manually answer for payment. One example of this is Amazon's Mechanical Turk, a website where businesses (or "requesters") will remotely hire individuals(known as "Turkers" or "crowdsourcers") to perform human intelligence tasks (tasks that computers cannot do). In theory, it is effective in processing high volumes of small tasks that would be expensive to achieve in other methods.<br />
<br />
The primary limitation of this method to acquire data is that respondents can submit incorrect responses so that we couldn't ensure the data quality.<br />
<br />
Therefore, the success of crowdsourcing is limited by how well ground-truth can be determined. The primary method for doing so is probabilistic inference. However, current methods are computationally expensive, lack theoretical guarantees, or are limited to specific settings. In the meantime, there are some approaches to focus on how we sample the data from the crowd, rather than how we aggregate it to improve the accuracy of the system.<br />
<br />
== Dawid-Skene Model for Crowdsourcing ==<br />
The one-coin Dawid-Skene model is popular for contextualizing crowdsourcing problems. For task <math>i</math> in set <math>M</math>, let the ground-truth be the binary <math>y_i = {\pm 1}</math>. We get labels <math>X = {x_{ij}}</math> where <math>j \in N</math> is the index for that worker.<br />
<br />
At each time step <math>t</math>, a worker <math>j = a(t) </math> provides their label for an assigned task <math>i</math> and provides the label <math>x_{ij} = {\pm 1}</math>. We denote responses up to time <math>t</math> via superscript.<br />
<br />
We let <math>x_{ij} = 0</math> if worker <math>j</math> has not completed task <math>i</math>. We assume that <math>P(x_{ij} = y_i) = p_j</math>. This implies that each worker is independent and has equal probability of correctly labelling regardless of task. In crowdsourcing the data, we must determine how workers are assigned to tasks. We introduce two methods.<br />
<br />
Under uniform sampling, workers are allocated to tasks such that each task is completed by the same number of workers, rounded to the nearest integer, and no worker completes a task more than once. This policy is given by <center><math>\pi_{uni}(t) = {\rm argmin}_{i \notin M_{a(t)}^t}\{ | N_i^t | \}.</math></center><br />
<br />
Under uncertainty sampling, we assign more workers to tasks that are less certain. Assuming, we are able to estimate the posterior probability of ground-truth, we can allocate workers to the task with the lowest probability of falling into the predicted class. This policy is given by <center><math>\pi_{us}(t) = argmin_{i \notin M_{a(t)}^t}\{ (max_{k \in \{\pm 1\}} ( P(y_i = k | X^t) ) \}.</math></center><br />
<br />
We then need to aggregate the data. The simple method of majority voting makes predictions for a given task based on the class the most workers have assigned it, <math>\hat{y}_i = \text{sign}\{\sum_{j \in N_i} x_{ij}\}</math>.<br />
<br />
== Streaming Bayesian Inference for Crowdsourced Classification (SBIC) ==<br />
The aim of the SBIC algorithm is to estimate the posterior probability, <math>P(y, p | X^t, \theta)</math> where <math>X^t</math> are the observed responses at time <math>t</math> and <math>\theta</math> is our prior. We can then generate predictions <math>\hat{y}^t</math> as the marginal probability over each <math>y_i</math> given <math>X^t</math>, and <math>\theta</math>.<br />
<br />
We factor <math>P(y, p | X^t, \theta) \approx \prod_{i \in M} \mu_i^t (y_i) \prod_{j \in N} \nu_j^t (p_j) </math> where <math>\mu_i^t</math> corresponds to each task and <math>\nu_j^t</math> to each worker.<br />
<br />
We then sequentially optimize the factors <math>\mu^t</math> and <math>\nu^t</math>. We begin by assuming that the worker accuracy follows a beta distribution with parameters <math>\alpha</math> and <math>\beta</math>. Initialize the task factors <math>\mu_i^0(+1) = q</math> and <math>\mu_i^0(-1) = 1 – q</math> for all <math>i</math>.<br />
<br />
When a new label is observed at time <math>t</math>, we update the <math>\nu_j^t</math> of worker <math>j</math>. We then update <math>\mu_i</math>. These updates are given by<br />
<br />
<center><math>\nu_j^t(p_j) \sim \text{Beta}(\sum_{i \in M_j^{t - 1}} \mu_i^{t - 1}(x_{ij}) + \alpha, \sum_{i \in M_j^{t - 1}} \mu_i^{t - 1}(-x_{ij}) + \beta) </math></center><br />
<br />
<center><math>\mu_i^t(y_i) \propto \begin{cases} \mu_i^{t - 1}(y_i)\overline{p}_j^t & x_{ij} = y_i \\ \mu_i^{t - 1}(y_i)(1 - \overline{p}_j^t) & x_{ij} \ne y_i \end{cases}</math></center><br />
where <math>\hat{p}_j^t = \frac{\sum_{i \in M_j^{t - 1}} \mu_i^{t - 1}(x_{ij}) + \alpha}{|M_j^{t - 1}| + \alpha + \beta }</math>.<br />
<br />
We choose our predictions to be the maximum <math>\mu_i^t(k) </math> for <math>k= \{-1,1\}</math>.<br />
<br />
Depending on our ordering of labels <math>X</math>, we can select for different applications.<br />
<br />
== Fast SBIC ==<br />
The pseudocode for Fast SBIC is shown below.<br />
<br />
<center>[[Image:FastSBIC.png|800px|]]</center><br />
<br />
As the name implies, the goal of this algorithm is speed. To facilitate this, we leave the order of <math>X</math> unchanged.<br />
<br />
We express <math>\mu_i^t</math> in terms of its log-odds<br />
<center><math>z_i^t = \log(\frac{\mu_i^t(+1)}{ \mu_i^t(-1)}) = z_i^{t - 1} + x_{ij} \log(\frac{\overline{p}_j^t}{1 - \overline{p}_j^t })</math></center><br />
where <math>z_i^0 = \log(\frac{q}{1 - q})</math>.<br />
<br />
The product chain then becomes a summation and removes the need to normalize each <math>\mu_i^t</math>. We use these log-odds to compute worker accuracy,<br />
<br />
<center><math>\overline{p}_j^t = \frac{\sum_{i \in M_j^{t - 1}} \sigma(x_{ij} z_i^{t-1}) + \alpha}{|M_j^{t - 1}| + \alpha + \beta}</math></center><br />
where <math>\sigma(z_i^{t-1}) := \frac{1}{1 + exp(-z_i^{t - 1})} = \mu_i^{t - 1}(+1) </math><br />
<br />
The final predictions are made by choosing class <math>\hat{y}_i^T = \text{sign}(z_i^T) </math>. We see later that Fast SBIC has similar computational speed to majority voting.<br />
<br />
== Sorted SBIC ==<br />
To increase the accuracy of the SBIC algorithm in exchange for computational efficiency, we run the algorithm in parallel giving labels in different orders. The pseudocode for this algorithm is given below.<br />
<br />
<center>[[Image:SortedSBIC.png|800px|]]</center><br />
<br />
From the general discussion of SBIC, we know that predictions on task <math>i</math> are more accurate toward the end of the collection process. This is a result of observing more data points and having run more updates on <math>\mu_i^t</math> and <math>\nu_j^t</math> to move them further from their prior. This means that task <math>i</math> is predicted more accurately when its corresponding labels are seen closer to the end of the process.<br />
<br />
We take advantage of this property by maintaining a distinct “view” of the log-odds for each task. When a label is observed, we update views for all tasks except the one for which the label was observed. At the end of the collection process, we process skipped labels. When run online, this process must be repeated at every timestep.<br />
<br />
We see that sorted SBIC is slower than Fast SBIC by a factor of M, the number of tasks. However, we can reduce the complexity by viewing <math>s^k</math> across different tasks in an offline setting when the whole dataset is known in advance.<br />
<br />
== Theoretical Analysis ==<br />
The authors prove an exponential relationship between the error probability and the number of labels per task. This allows for an upper bound to be placed on the error, in the asymptotic regime, where it can be assumed the SBIC predictions are close to the true values. The two theorems, for the different sampling regimes, are presented below.<br />
<br />
<center>[[Image:Theorem1.png|800px|]]</center><br />
<br />
<center>[[Image:Theorem2.png|800px|]]</center><br />
<br />
== Empirical Analysis ==<br />
The purpose of the empirical analysis is to compare SBIC to the existing state of the art algorithms. The SBIC algorithm is run on five real-world binary classification datasets. The results can be found in the table below. Other algorithms in the comparison are, from left to right, majority voting, expectation-maximization, mean-field, belief-propagation, Monte-Carlo sampling, and triangular estimation. <br />
<br />
First of all, the algorithms are run on a synthetic data that meets the assumptions of an underlying one-coin Dawid-Skene model, which allows the authors to compare SBIC's performance empirically with the theoretical results previously shown. <br />
<br />
<center>[[Image:RealWorldResults.png|800px|]]</center><br />
<br />
In bold are the best performing algorithms for each dataset. We see that both versions of the SBIC algorithm are competitive, having similar prediction errors to EM, AMF, and MC. All are considered state-of-the-art Bayesian algorithms.<br />
<br />
The figure below shows the average time required to simulate predictions on synthetic data under an uncertainty sampling policy. We see that Fast SBIC is comparable to majority voting and significantly faster than the other algorithms. This speed improvement, coupled with comparable accuracy, makes the Fast SBIC algorithm powerful.<br />
<br />
<center>[[Image:TimeRequirement.png|800px|]]</center><br />
<br />
== Conclusion and Future Research ==<br />
In conclusion, we have seen that SBIC is computationally efficient, accurate in practice, and has theoretical guarantees. The authors intend to extend the algorithm to the multi-class case in the future.<br />
<br />
== Critique ==<br />
In crowdsourcing data, the cost associated with collecting additional labels is not usually prohibitively expensive. As a result, if there is concern over ground-truth, paying for additional data to ensure <math>X</math> is sufficiently dense may be the desired response as opposed to sacrificing ground-truth accuracy. This may result in the SBIC algorithm being less practically useful than intended.Perhaps, a study can be done to compare the cost of acquiring additional data and checking how much it improves the accuracy of ground-truth. This can help us decide the usefulness of this algorithm.Second, SBIC should be used in multiple types of data like audio, text and images to make sure that it delivers consistent results. <br />
<br />
The paper is tackling the classic problem of aggregating labels in a crowdsourced application, with a focus on speed. The algorithms proposed are fast and simple to implement and come with theoretical guarantees on the bounds for error rates. However, the paper starts with an objective of designing fast label aggregation algorithms for a streaming setting yet doesn’t spend any time motivating the applications in which such algorithms are needed. All the datasets used in the empirical analysis are static datasets therefore for the paper to be useful, the problem considered should be well motivated. It also appears that the output from the algorithm depends on the order in which the data is processed, which may need to be clarified. Finally, the theoretical results are presented under the assumption that the predictions of the FBI converge to the ground truth, however, the reasoning behind this assumption is not explained.<br />
<br />
The paper assumes that crowdsourcing from human beings is systematic: that is, respondents to the problems would act in similar ways that can be classified into some categories. There are lots of other factors that need to be considered for a human respondent, such as fatigue effects and conflicts of interest. Those factors would seriously jeopardize the validity of the results and the model if they were not carefully designed and taken care of. For example, one formally accurate subject reacts badly to the subject one day generating lots of faulty data, and it would take lots of correct votes to even out the effects. Even in lots of medical experiment that involves human subjects, with rigorous standards and procedures, the results could still be invalid. The trade-off for speed while sacrificing validity of results is not wise.<br />
<br />
== References ==<br />
[1] Manino, Tran-Thanh, and Jennings. Streaming Bayesian Inference for Crowdsourced Classification. 33rd Conference on Neural Information Processing Systems, 2019</div>Mhamdyhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Streaming_Bayesian_Inference_for_Crowdsourced_Classification&diff=46189Streaming Bayesian Inference for Crowdsourced Classification2020-11-24T03:38:47Z<p>Mhamdy: /* Dawid-Skene Model for Crowdsourcing */</p>
<hr />
<div>Group 4 Paper Presentation Summary<br />
<br />
By Jonathan Chow, Nyle Dharani, Ildar Nasirov<br />
<br />
== Motivation ==<br />
Crowdsourcing can be a useful tool for data generation in classification projects by collecting annotations of large groups. Typically, this takes the form of online questions which many respondents will manually answer for payment. One example of this is Amazon's Mechanical Turk, a website where businesses (or "requesters") will remotely hire individuals(known as "Turkers" or "crowdsourcers") to perform human intelligence tasks (tasks that computers cannot do). In theory, it is effective in processing high volumes of small tasks that would be expensive to achieve in other methods.<br />
<br />
The primary limitation of this method to acquire data is that respondents can submit incorrect responses so that we couldn't ensure the data quality.<br />
<br />
Therefore, the success of crowdsourcing is limited by how well ground-truth can be determined. The primary method for doing so is probabilistic inference. However, current methods are computationally expensive, lack theoretical guarantees, or are limited to specific settings. In the meantime, there are some approaches to focus on how we sample the data from the crowd, rather than how we aggregate it to improve the accuracy of the system.<br />
<br />
== Dawid-Skene Model for Crowdsourcing ==<br />
The one-coin Dawid-Skene model is popular for contextualizing crowdsourcing problems. For task <math>i</math> in set <math>M</math>, let the ground-truth be the binary <math>y_i = {\pm 1}</math>. We get labels <math>X = {x_{ij}}</math> where <math>j \in N</math> is the index for that worker.<br />
<br />
At each time step <math>t</math>, a worker <math>j = a(t) </math> provides their label for an assigned task <math>i</math> and provides the label <math>x_{ij} = {\pm 1}</math>. We denote responses up to time <math>t</math> via superscript.<br />
<br />
We let <math>x_{ij} = 0</math> if worker <math>j</math> has not completed task <math>i</math>. We assume that <math>P(x_{ij} = y_i) = p_j</math>. This implies that each worker is independent and has equal probability of correctly labelling regardless of task. In crowdsourcing the data, we must determine how workers are assigned to tasks. We introduce two methods.<br />
<br />
Under uniform sampling, workers are allocated to tasks such that each task is completed by the same number of workers, rounded to the nearest integer, and no worker completes a task more than once. This policy is given by <center><math>\pi_{uni}(t) = argmin_{i \notin M_{a(t)}^t}\{ | N_i^t | \}.</math></center><br />
<br />
Under uncertainty sampling, we assign more workers to tasks that are less certain. Assuming, we are able to estimate the posterior probability of ground-truth, we can allocate workers to the task with the lowest probability of falling into the predicted class. This policy is given by <center><math>\pi_{us}(t) = argmin_{i \notin M_{a(t)}^t}\{ (max_{k \in \{\pm 1\}} ( P(y_i = k | X^t) ) \}.</math></center><br />
<br />
We then need to aggregate the data. The simple method of majority voting makes predictions for a given task based on the class the most workers have assigned it, <math>\hat{y}_i = \text{sign}\{\sum_{j \in N_i} x_{ij}\}</math>.<br />
<br />
== Streaming Bayesian Inference for Crowdsourced Classification (SBIC) ==<br />
The aim of the SBIC algorithm is to estimate the posterior probability, <math>P(y, p | X^t, \theta)</math> where <math>X^t</math> are the observed responses at time <math>t</math> and <math>\theta</math> is our prior. We can then generate predictions <math>\hat{y}^t</math> as the marginal probability over each <math>y_i</math> given <math>X^t</math>, and <math>\theta</math>.<br />
<br />
We factor <math>P(y, p | X^t, \theta) \approx \prod_{i \in M} \mu_i^t (y_i) \prod_{j \in N} \nu_j^t (p_j) </math> where <math>\mu_i^t</math> corresponds to each task and <math>\nu_j^t</math> to each worker.<br />
<br />
We then sequentially optimize the factors <math>\mu^t</math> and <math>\nu^t</math>. We begin by assuming that the worker accuracy follows a beta distribution with parameters <math>\alpha</math> and <math>\beta</math>. Initialize the task factors <math>\mu_i^0(+1) = q</math> and <math>\mu_i^0(-1) = 1 – q</math> for all <math>i</math>.<br />
<br />
When a new label is observed at time <math>t</math>, we update the <math>\nu_j^t</math> of worker <math>j</math>. We then update <math>\mu_i</math>. These updates are given by<br />
<br />
<center><math>\nu_j^t(p_j) \sim \text{Beta}(\sum_{i \in M_j^{t - 1}} \mu_i^{t - 1}(x_{ij}) + \alpha, \sum_{i \in M_j^{t - 1}} \mu_i^{t - 1}(-x_{ij}) + \beta) </math></center><br />
<br />
<center><math>\mu_i^t(y_i) \propto \begin{cases} \mu_i^{t - 1}(y_i)\overline{p}_j^t & x_{ij} = y_i \\ \mu_i^{t - 1}(y_i)(1 - \overline{p}_j^t) & x_{ij} \ne y_i \end{cases}</math></center><br />
where <math>\hat{p}_j^t = \frac{\sum_{i \in M_j^{t - 1}} \mu_i^{t - 1}(x_{ij}) + \alpha}{|M_j^{t - 1}| + \alpha + \beta }</math>.<br />
<br />
We choose our predictions to be the maximum <math>\mu_i^t(k) </math> for <math>k= \{-1,1\}</math>.<br />
<br />
Depending on our ordering of labels <math>X</math>, we can select for different applications.<br />
<br />
== Fast SBIC ==<br />
The pseudocode for Fast SBIC is shown below.<br />
<br />
<center>[[Image:FastSBIC.png|800px|]]</center><br />
<br />
As the name implies, the goal of this algorithm is speed. To facilitate this, we leave the order of <math>X</math> unchanged.<br />
<br />
We express <math>\mu_i^t</math> in terms of its log-odds<br />
<center><math>z_i^t = \log(\frac{\mu_i^t(+1)}{ \mu_i^t(-1)}) = z_i^{t - 1} + x_{ij} \log(\frac{\overline{p}_j^t}{1 - \overline{p}_j^t })</math></center><br />
where <math>z_i^0 = \log(\frac{q}{1 - q})</math>.<br />
<br />
The product chain then becomes a summation and removes the need to normalize each <math>\mu_i^t</math>. We use these log-odds to compute worker accuracy,<br />
<br />
<center><math>\overline{p}_j^t = \frac{\sum_{i \in M_j^{t - 1}} \sigma(x_{ij} z_i^{t-1}) + \alpha}{|M_j^{t - 1}| + \alpha + \beta}</math></center><br />
where <math>\sigma(z_i^{t-1}) := \frac{1}{1 + exp(-z_i^{t - 1})} = \mu_i^{t - 1}(+1) </math><br />
<br />
The final predictions are made by choosing class <math>\hat{y}_i^T = \text{sign}(z_i^T) </math>. We see later that Fast SBIC has similar computational speed to majority voting.<br />
<br />
== Sorted SBIC ==<br />
To increase the accuracy of the SBIC algorithm in exchange for computational efficiency, we run the algorithm in parallel giving labels in different orders. The pseudocode for this algorithm is given below.<br />
<br />
<center>[[Image:SortedSBIC.png|800px|]]</center><br />
<br />
From the general discussion of SBIC, we know that predictions on task <math>i</math> are more accurate toward the end of the collection process. This is a result of observing more data points and having run more updates on <math>\mu_i^t</math> and <math>\nu_j^t</math> to move them further from their prior. This means that task <math>i</math> is predicted more accurately when its corresponding labels are seen closer to the end of the process.<br />
<br />
We take advantage of this property by maintaining a distinct “view” of the log-odds for each task. When a label is observed, we update views for all tasks except the one for which the label was observed. At the end of the collection process, we process skipped labels. When run online, this process must be repeated at every timestep.<br />
<br />
We see that sorted SBIC is slower than Fast SBIC by a factor of M, the number of tasks. However, we can reduce the complexity by viewing <math>s^k</math> across different tasks in an offline setting when the whole dataset is known in advance.<br />
<br />
== Theoretical Analysis ==<br />
The authors prove an exponential relationship between the error probability and the number of labels per task. This allows for an upper bound to be placed on the error, in the asymptotic regime, where it can be assumed the SBIC predictions are close to the true values. The two theorems, for the different sampling regimes, are presented below.<br />
<br />
<center>[[Image:Theorem1.png|800px|]]</center><br />
<br />
<center>[[Image:Theorem2.png|800px|]]</center><br />
<br />
== Empirical Analysis ==<br />
The purpose of the empirical analysis is to compare SBIC to the existing state of the art algorithms. The SBIC algorithm is run on five real-world binary classification datasets. The results can be found in the table below. Other algorithms in the comparison are, from left to right, majority voting, expectation-maximization, mean-field, belief-propagation, Monte-Carlo sampling, and triangular estimation. <br />
<br />
First of all, the algorithms are run on a synthetic data that meets the assumptions of an underlying one-coin Dawid-Skene model, which allows the authors to compare SBIC's performance empirically with the theoretical results previously shown. <br />
<br />
<center>[[Image:RealWorldResults.png|800px|]]</center><br />
<br />
In bold are the best performing algorithms for each dataset. We see that both versions of the SBIC algorithm are competitive, having similar prediction errors to EM, AMF, and MC. All are considered state-of-the-art Bayesian algorithms.<br />
<br />
The figure below shows the average time required to simulate predictions on synthetic data under an uncertainty sampling policy. We see that Fast SBIC is comparable to majority voting and significantly faster than the other algorithms. This speed improvement, coupled with comparable accuracy, makes the Fast SBIC algorithm powerful.<br />
<br />
<center>[[Image:TimeRequirement.png|800px|]]</center><br />
<br />
== Conclusion and Future Research ==<br />
In conclusion, we have seen that SBIC is computationally efficient, accurate in practice, and has theoretical guarantees. The authors intend to extend the algorithm to the multi-class case in the future.<br />
<br />
== Critique ==<br />
In crowdsourcing data, the cost associated with collecting additional labels is not usually prohibitively expensive. As a result, if there is concern over ground-truth, paying for additional data to ensure <math>X</math> is sufficiently dense may be the desired response as opposed to sacrificing ground-truth accuracy. This may result in the SBIC algorithm being less practically useful than intended.Perhaps, a study can be done to compare the cost of acquiring additional data and checking how much it improves the accuracy of ground-truth. This can help us decide the usefulness of this algorithm.Second, SBIC should be used in multiple types of data like audio, text and images to make sure that it delivers consistent results. <br />
<br />
The paper is tackling the classic problem of aggregating labels in a crowdsourced application, with a focus on speed. The algorithms proposed are fast and simple to implement and come with theoretical guarantees on the bounds for error rates. However, the paper starts with an objective of designing fast label aggregation algorithms for a streaming setting yet doesn’t spend any time motivating the applications in which such algorithms are needed. All the datasets used in the empirical analysis are static datasets therefore for the paper to be useful, the problem considered should be well motivated. It also appears that the output from the algorithm depends on the order in which the data is processed, which may need to be clarified. Finally, the theoretical results are presented under the assumption that the predictions of the FBI converge to the ground truth, however, the reasoning behind this assumption is not explained.<br />
<br />
The paper assumes that crowdsourcing from human beings is systematic: that is, respondents to the problems would act in similar ways that can be classified into some categories. There are lots of other factors that need to be considered for a human respondent, such as fatigue effects and conflicts of interest. Those factors would seriously jeopardize the validity of the results and the model if they were not carefully designed and taken care of. For example, one formally accurate subject reacts badly to the subject one day generating lots of faulty data, and it would take lots of correct votes to even out the effects. Even in lots of medical experiment that involves human subjects, with rigorous standards and procedures, the results could still be invalid. The trade-off for speed while sacrificing validity of results is not wise.<br />
<br />
== References ==<br />
[1] Manino, Tran-Thanh, and Jennings. Streaming Bayesian Inference for Crowdsourced Classification. 33rd Conference on Neural Information Processing Systems, 2019</div>Mhamdyhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Influenza_Forecasting_Framework_based_on_Gaussian_Processes&diff=44899Influenza Forecasting Framework based on Gaussian Processes2020-11-16T05:42:13Z<p>Mhamdy: /* References */</p>
<hr />
<div><br />
== Abstract ==<br />
<br />
This paper presents a novel framework for seasonal epidemic forecasting using Gaussian process regression. Resulting retrospective forecasts, trained on a subset of the publicly available CDC influenza-like-illness (ILI) data-set, outperformed four state-of-the-art models when compared using the official CDC scoring rule (log-score).<br />
<br />
== Background ==<br />
<br />
Each year, the seasonal influenza epidemic affects public health at a massive scale, resulting in 38 million cases, 400 000 hospitalizations, and 22 000 deaths in the United States in 2019/20 alone ([https://www.cdc.gov/flu/about/burden/2019-2020.html#flu-burden-infographic]). Given this, reliable forecasts of future influenza development are invaluable, because they allow for improved public health policies and informed resource development and allocation.<br />
<br />
== Related Work ==<br />
<br />
Given the value of epidemic forecasts, the CDC regularly publishes ILI data and has funded a seasonal ILI forecasting challenge. This challenge has lead to four state of the art models in the field; MSS, a physical susceptible-infected-recovered model with assumed linear noise [4]; SARIMA, a framework based on seasonal auto-regressive moving average models [2]; and LinEns, an ensemble of three linear regression models.<br />
<br />
== Motivation ==<br />
<br />
It has been shown that LinEns forecasts outperform the other frameworks on the ILI data-set. However, this framework assumes a deterministic relationship between the epidemic week and its case count, which does not reflect the stochastic nature of the trend. Therefore, it is natural to ask whether a similar framework that assumes a stochastic relationship between these variables would provide better performance. This motivated the development of the proposed Gaussian process regression framework, and the subsequent performance comparison to the benchmark models.<br />
<br />
== Gaussian Process Regression ==<br />
<br />
Consider the following set up: let <math>X = [\mathbf{x}_1,\ldots,\mathbf{x}_n]</math> <math>(d\times n)</math> be your training data, <math>\mathbf{y} = [y_1,y_2,\ldots,y_n]^T</math> be your noisy observations where <math>y_i = f(\mathbf{x}_i) + \epsilon_i</math>, <math>(\epsilon_i:i = 1,\ldots,n)</math> i.i.d. <math>\sim \mathcal{N}(0,{\sigma}^2)</math>, and <math>f</math> is the trend we are trying to model (by <math>\hat{f}</math>). Let <math>\mathbf{x}^*</math> <math>(d\times 1)</math> be your test data point, and <math>\hat{y} = \hat{f}(\mathbf{x}^*)</math> be your predicted outcome.<br />
<br />
<br />
Instead of assuming a deterministic form of <math>f</math>, and thus of <math>\mathbf{y}</math> and <math>\hat{y}</math> (as classical linear regression would, for example), Gaussian process regression assumes <math>f</math> is stochastic. More precisely, <math>\mathbf{y}</math> and <math>\hat{y}</math> are assumed to have a joint prior distribution. Indeed, we have <br />
<br />
$$<br />
(\mathbf{y},\hat{y}) \sim \mathcal{N}(0,\Sigma(X,\mathbf{x}^*))<br />
$$<br />
<br />
where <math>\Sigma(X,\mathbf{x}^*)</math> is a matrix of covariances dependent on some kernel function <math>k</math>. In this paper, the kernel function is assumed to be Gaussian and takes the form <br />
<br />
$$<br />
k(\mathbf{x}_i,\mathbf{x}_j) = \sigma^2\exp(-\frac{1}{2}(\mathbf{x}_i-\mathbf{x}^j)^T\Sigma(\mathbf{x}_i-\mathbf{x}_j)).<br />
$$<br />
<br />
It is important to note that this gives a joint prior distribution of '''functions''' ('''Fig. 1''' left, grey curves). <br />
<br />
By restricting this distribution to contain only those functions ('''Fig. 1''' right, grey curves) that agree with the observed data points <math>\mathbf{x}</math> ('''Fig. 1''' right, solid black) we obtain the posterior distribution for <math>\hat{y}</math> which has the form<br />
<br />
$$<br />
p(\hat{y} | \mathbf{x}^*, X, \mathbf{y}) \sim \mathcal{N}(\mu(\mathbf{x}^*,X,\mathbf{y}),\sigma(\mathbf{x}^*,X))<br />
$$<br />
<br />
<div style="text-align:center;"> [[File:GPRegression.png|500px]] </div><br />
<br />
<div align="center">'''Figure 1. Gaussian process regression''': Select the functions from your joint prior distribution (left, grey curves) with mean <math>0</math> (left, bold line) that agree with the observed data points (right, black bullets). These form your posterior distribution (right, grey curves) with mean <math>\mu(\mathbf{x})</math> (right, bold line). Red triangle helps compare the two images (location marker) [3]. </div><br />
<br />
== Data-set Description ==<br />
<br />
Let <math>d_j^i</math> denote the number of epidemic cases recorded in week <math>j</math> of season <math>i</math>, and let <math>j^*</math> and <math>i^*</math> denote the current week and season, respectively. The ILI data-set contains $d_j^i$ for all previous weeks and seasons, up to the current season with a 1-3 week publishing delay. Note that a season refers to the time of year when the epidemic is prevalent (e.g. an influenza season lasts 30 weeks and contains the last 10 weeks of year k, and the first 20 weeks of year k+1). The goal is to predict <math>\hat{y}_T = \hat{f}_T(x^*) = d^{i^*}_{j* + T}</math> where <math>T, \;(T = 1,\ldots,K)</math> is the target week (how many weeks into the future that you want to predict).<br />
<br />
<br />
To do this, a design matrix <math>X</math> is constructed where each element <math>X_{ji} = d_j^i</math> corresponds to the number of cases in week (row) j of season (column) i. The training outcomes <math>y_{i,T}, i = 1,\ldots,n</math> correspond to the number of cases that were observed in target week <math>T,\; (T = 1,\ldots,K)</math> of season <math>i, (i = 1,\ldots,n)</math>.<br />
<br />
== Proposed Framework ==<br />
<br />
To compute <math>\hat{y}</math>, the following algorithm is executed. <br />
<br />
<ol><br />
<br />
<li> Let <math>J \subseteq \{j^*-4 \leq j \leq j^*\}</math> (subset of possible weeks).<br />
<br />
<li> Assemble the Training Set <math>\{X_J, \mathbf{y}_{T,J}\}</math> <br />
<br />
<li> Train the Gaussian process<br />
<br />
<li> Calculate the '''distribution''' of <math>\hat{y}_{T,J}</math> using <math>p(\hat{y}_{T,J} | \mathbf{x}^*, X_J, \mathbf{y}_{T,J}) \sim \mathcal{N}(\mu(\mathbf{x}^*,X,\mathbf{y}_{T,J}),\sigma(\mathbf{x}^*,X_J))</math><br />
<br />
<li> Set <math>\hat{y}_{T,J} =\mu(x^*,X_J,\mathbf{y}_{T,J})</math><br />
<br />
<li> Repeat steps 2-5 for all sets of weeks <math>J</math><br />
<br />
<li> Determine the best 3 performing sets J (on the 2010/11 and 2011/12 validation sets)<br />
<br />
<li> Calculate the ensemble forecast by averaging the 3 best performing predictive distribution densities i.e. <math>\hat{y}_T = \frac{1}{3}\sum_{k=1}^3 \hat{y}_{T,J_{best}}</math><br />
<br />
</ol><br />
<br />
== Results ==<br />
<br />
To demonstrate the accuracy of their results, retrospective forecasting was done on the ILI data-set. In other words, the Gaussian process model was trained assuming a previous season (2012/13) was the current season. In this fashion, the forecast could be compared to the already observed true outcome. <br />
<br />
To produce a forecast for the entire 2012/13 season, 30 Gaussian processes were trained (each influenza season has 30 test points <math>\mathbf{x^*}</math>) and a curve connecting the predicted outputs <math>y_T = \hat{f}(\mathbf{x^*)}</math> was plotted ('''Fig.2''', blue line). As shown in '''Fig.2''', this forecast (blue line) was reliable for both 1 (left) and 3 (right) week targets, given that the 95% prediction interval ('''Fig.2''', purple shaded) contained the true values ('''Fig.2''', red x's) 95% of the time.<br />
<br />
<div style="text-align:center;"> [[File:ResultsOne.png|600px]] </div><br />
<br />
<div align="center">'''Figure 2. Retrospective forecasts and their uncertainty''': One week retrospective influenza forecasting for two targets (T = 1, 3). Red x’s are the true observed values, and blue lines and purple shaded areas represent point forecasts and 95% prediction intervals, respectively. </div><br />
<br />
<br />
Moreover, as shown in '''Fig.3''', the novel Gaussian process regression framework outperformed all benchmarks for four different targets <math>(T = 1,\ldots, 4)</math> , including LinEns, when compared using the official CDC scoring criterion ''log-score''. Log-score describes the logarithmic probability of the forecast being within in an interval around the true value. <br />
<br />
<div style="text-align:center;"> [[File:ComparisonNew.png|600px]] </div><br />
<br />
<div align="center">'''Figure 3. Average log-score gain of proposed framework''': Each bar shows the mean seasonal log-score gain of the proposed framework vs. the given state-of-the-art model, and each panel corresponds to a different target week <math> T = 1,...4 </math>. </div><br />
<br />
== Conclusion ==<br />
<br />
This paper presented a novel framework for forecasting seasonal epidemics using Gaussian process regression that outperformed multiple state-of-the-art forecasting methods on the CDC's ILI data-set. Hence, this work may play a key role in future influenza forecasting and as result, the improvement of public health policies and resource allocation.<br />
<br />
== Critique ==<br />
<br />
The proposed framework provides a computationally efficient method to forecast any seasonal epidemic count data that is easily extendable to multiple target types. In particular; one can compute key parameters such as the peak infection incidence (<math>\hat{y} = max_{0 \leq j \leq 52} d^i_j </math>), the timing of the peak infection incidence (<math>\hat{y} = argmax_{0 \leq j \leq 52} d^i_j</math>) and the final epidemic size of a season (<math>\hat{y} = \sum_{j=1}^{52} d^i_j</math>). However, given it is not a physical model, it cannot provide insights on parameters describing the disease spread. Moreover, the framework requires training data and hence, is not applicable for non-seasonal epidemics.<br />
<br />
== References ==<br />
<br />
[1] CDC website https://www.cdc.gov/flu/about/burden/2019-2020.html#flu-burden-infographic<br />
<br />
[2] Ray, E. L., Sakrejda, K., Lauer, S. A., Johansson, M. A.,and Reich, N. G. (2017).Infectious disease prediction with kernel conditional densityestimation.Statistics in Medicine, 36(30):4908–4929.<br />
<br />
[3] Schulz, E., Speekenbrink, M., and Krause, A. (2017).A tutorial on gaussian process regression with a focus onexploration-exploitation scenarios.bioRxiv.<br />
<br />
[4] Zimmer, C., Leuba, S. I., Cohen, T., and Yaesoubi, R.(2019).Accurate quantification of uncertainty in epidemicparameter estimates and predictions using stochasticcompartmental models.Statistical Methods in Medical Research,28(12):3591–3608.PMID: 30428780.</div>Mhamdyhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat940F21&diff=42840stat940F212020-10-26T19:58:57Z<p>Mhamdy: </p>
<hr />
<div>== [[F20-STAT 946-Proposal| Project Proposal ]] ==<br />
<br />
<br />
= Record your contributions here [https://docs.google.com/spreadsheets/d/1Me_O000pNxeTwNGEac57XakecG1wahvwGE5n36DGIlM/edit?usp=sharing]=<br />
<br />
Use the following notations:<br />
<br />
P: You have written a summary/critique on the paper.<br />
<br />
T: You had a technical contribution on a paper (excluding the paper that you present).<br />
<br />
E: You had an editorial contribution on a paper (excluding the paper that you present).<br />
<br />
<br />
=Paper presentation=<br />
{| class="wikitable"<br />
<br />
{| border="1" cellpadding="3"<br />
|-<br />
|width="60pt"|Date<br />
|width="100pt"|Name <br />
|width="30pt"|Paper number <br />
|width="700pt"|Title<br />
|width="30pt"|Link to the paper<br />
|width="30pt"|Link to the summary<br />
|width="30pt"|Link to the video<br />
|-<br />
|-<br />
|Sep 15 (example)||Ri Wang || ||Sequence to sequence learning with neural networks.||[http://papers.nips.cc/paper/5346-sequence-to-sequence-learning-with-neural-networks.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Going_Deeper_with_Convolutions Summary] || [https://youtu.be/JWozRg_X-Vg?list=PLehuLRPyt1HzXDemu7K4ETcF0Ld_B5adG&t=539]<br />
|-<br />
|Week of Nov 2 || Jose Avilez || 1|| Gradientless Descent: High-Dimensional Zeroth-Order Optimisation || [https://openreview.net/pdf?id=Skep6TVYDB] || ||<br />
|-<br />
|Week of Nov 2 || Abhinav Chanana || 2||AUGMIX: A Simple Data Procession method to Improve Robustness And Uncertainity || [https://openreview.net/pdf?id=S1gmrxHFvB Paper] || ||<br />
|-<br />
|Week of Nov 2 || Maziar Dadbin || 3|| ALBERT: A Lite BERT for Self-supervised Learning of Language Representations || https://openreview.net/pdf?id=H1eA7AEtvS || ||<br />
|-<br />
|Week of Nov 2 ||John Edwards || 4||Learn, Imagine and Create: Text-to-Image Generation from Prior Knowledge ||[https://papers.nips.cc/paper/8375-learn-imagine-and-create-text-to-image-generation-from-prior-knowledge.pdf Paper] || ||<br />
|-<br />
|Week of Nov 2 ||Wenyu Shen || 5|| STRUCTBERT:INCORPORATING LANGUAGE STRUCTURES INTO PRETRAINING FOR DEEP LANGUAGE UNDERSTANDING || [https://openreview.net/pdf?id=BJgQ4lSFPH] || ||<br />
|-<br />
|Week of Nov 2 || Syed Saad Naseem || 6|| Learning The Difference That Makes A Difference With Counterfactually-Augmented Data|| [https://openreview.net/pdf?id=Sklgs0NFvr Paper] || ||<br />
|-<br />
|Week of Nov 9 || Donya Hamzeian || 7|| The Curious Case of Neural Text Degeneration || https://iclr.cc/virtual_2020/poster_rygGQyrFvH.html || ||<br />
|-<br />
|Week of Nov 9 || Parsa Torabian || 8|| Orthogonal Gradient Descent for Continual Learning || [http://proceedings.mlr.press/v108/farajtabar20a/farajtabar20a.pdf Paper] || ||<br />
|-<br />
|Week of Nov 9 || Arash Moayyedi || 9|| When Does Self-supervision Improve Few-shot Learning? || [https://openreview.net/forum?id=HkenPn4KPH Paper] || ||<br />
|-<br />
|Week of Nov 9 || Parsa Ashrafi Fashi || 10|| Probabilistic Model-Agnostic Meta-Learning || [http://papers.nips.cc/paper/8161-probabilistic-model-agnostic-meta-learning.pdf Paper] || ||<br />
|-<br />
|Week of Nov 9 || Jaskirat Singh Bhatia || 11|| A FAIRCOMPARISON OFGRAPHNEURALNETWORKSFORGRAPHCLASSIFICATION || [https://openreview.net/pdf?id=HygDF6NFPB Paper] || ||<br />
|-<br />
|Week of Nov 9 || Gaurav Sikri || 12|| EMPIRICAL STUDIES ON THE PROPERTIES OF LINEAR REGIONS IN DEEP NEURAL NETWORKS || [https://openreview.net/pdf?id=SkeFl1HKwr Paper] || ||<br />
|-<br />
|Week of Nov 16 || Abhinav Jain || 13|| The Logical Expressiveness of Graph Neural Networks || [http://www.openreview.net/pdf?id=r1lZ7AEKvB Paper] || ||<br />
|-<br />
|Week of Nov 16 || Gautam Bathla || 14|| One-Shot Object Detection with Co-Attention and Co-Excitation || [https://papers.nips.cc/paper/8540-one-shot-object-detection-with-co-attention-and-co-excitation.pdf Paper] || ||<br />
|-<br />
|Week of Nov 16 || Shikhar Sakhuja || 15|| SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems || [https://papers.nips.cc/paper/8589-superglue-a-stickier-benchmark-for-general-purpose-language-understanding-systems.pdf Paper] || ||<br />
|-<br />
|Week of Nov 16 || Cameron Meaney || 16|| Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations || [https://www.sciencedirect.com/science/article/pii/S0021999118307125 Paper] || ||<br />
|-<br />
|Week of Nov 16 ||Sobhan Hemati|| 17||Adversarial Fisher Vectors for Unsupervised Representation Learning||[https://papers.nips.cc/paper/9295-adversarial-fisher-vectors-for-unsupervised-representation-learning.pdf Paper]|| ||<br />
|-<br />
|Week of Nov 16 ||Milad Sikaroudi|| 18||Domain Genralization via Model Agnostic Learning of Semantic Features||[https://papers.nips.cc/paper/8873-domain-generalization-via-model-agnostic-learning-of-semantic-features.pdf Paper]|| ||<br />
|-<br />
|Week of Nov 23 ||Bowen You|| 19||DREAM TO CONTROL: LEARNING BEHAVIORS BY LATENT IMAGINATION||[https://openreview.net/pdf?id=S1lOTC4tDS Paper]|| ||<br />
|-<br />
|Week of Nov 23 ||Nouha Chatti|| 20|| This Looks Like That: Deep Learning for Interpretable Image Recognition||[https://papers.nips.cc/paper/9095-this-looks-like-that-deep-learning-for-interpretable-image-recognition.pdf Paper]|| ||<br />
|-<br />
|Week of Nov 23 || Mohan Wu || 21|| Pretrained Generalized Autoregressive Model with Adaptive Probabilistic Label Cluster for Extreme Multi-label Text Classification || [https://proceedings.icml.cc/static/paper_files/icml/2020/807-Paper.pdf Paper] || ||<br />
|-<br />
|Week of Nov 23 || Xinyi Yan || 22|| Incorporating BERT into Neural Machine Translation || [https://iclr.cc/virtual_2020/poster_Hyl7ygStwB.html Paper] || ||<br />
|-<br />
|Week of Nov 23 || Meixi Chen || 23|| Functional Regularisation for Continual Learning with Gaussian Processes || [https://arxiv.org/pdf/1901.11356.pdf Paper] || ||<br />
|-<br />
|Week of Nov 23 || Ahmed Salamah || 24|| Sparse Convolutional Neural Networks || [https://www.cv-foundation.org/openaccess/content_cvpr_2015/papers/Liu_Sparse_Convolutional_Neural_2015_CVPR_paper.pdf Paper] || ||<br />
|-<br />
|Week of Nov 23|| Mohammad Mahmoud || 32||Mathematical Reasoning in Latent Space|| [https://iclr.cc/virtual_2020/poster_Ske31kBtPr.html?fbclid=IwAR2TQkabQkOzGcMl6bEJYggq8X8HIUoTudPIACX2v_ZT2LteARl_sPD-XdQ] || |-<br />
|-<br />
|Week of Nov 30 ||Danial Maleki || 25||Attention Is All You Need ||[https://arxiv.org/abs/1706.03762 Paper] || ||<br />
|-<br />
|Week of Nov 30 ||Gursimran Singh || 26||BERTScore: Evaluating Text Generation with BERT. ||[https://openreview.net/pdf?id=SkeHuCVFDr Paper] || ||<br />
|-<br />
|Week of Nov 30 || Govind Sharma || 27|| Time-series Generative Adversarial Networks || [https://papers.nips.cc/paper/8789-time-series-generative-adversarial-networks.pdf Paper] || ||<br />
|-<br />
|Week of Nov 30 ||Maral Rasoolijaberi|| 28||Parameter-free, Dynamic, and Strongly-Adaptive Online Learning|| [https://proceedings.icml.cc/static/paper_files/icml/2020/2820-Paper.pdf Paper] || ||<br />
|-<br />
|Week of Nov 30 || Sina Farsangi || 29|| Boosting Few-Shot Visual Learning with Self-Supervision || https://openaccess.thecvf.com/content_ICCV_2019/papers/Gidaris_Boosting_Few-Shot_Visual_Learning_With_Self-Supervision_ICCV_2019_paper.pdf || ||<br />
|-<br />
|Week of Nov 30 || Pierre McWhannel || 30|| Pre-training Tasks for Embedding-based Large-scale Retrieval || [https://openreview.net/pdf?id=rkg-mA4FDr Paper] || placeholder||<br />
|-<br />
|Week of Nov 30 || Wenjuan Qi || 31|| Network Deconvolution || [https://openreview.net/pdf?id=rkeu30EtvS Paper] || placeholder||</div>Mhamdyhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat940F21&diff=42839stat940F212020-10-26T19:44:14Z<p>Mhamdy: </p>
<hr />
<div>== [[F20-STAT 946-Proposal| Project Proposal ]] ==<br />
<br />
<br />
= Record your contributions here [https://docs.google.com/spreadsheets/d/1Me_O000pNxeTwNGEac57XakecG1wahvwGE5n36DGIlM/edit?usp=sharing]=<br />
<br />
Use the following notations:<br />
<br />
P: You have written a summary/critique on the paper.<br />
<br />
T: You had a technical contribution on a paper (excluding the paper that you present).<br />
<br />
E: You had an editorial contribution on a paper (excluding the paper that you present).<br />
<br />
<br />
=Paper presentation=<br />
{| class="wikitable"<br />
<br />
{| border="1" cellpadding="3"<br />
|-<br />
|width="60pt"|Date<br />
|width="100pt"|Name <br />
|width="30pt"|Paper number <br />
|width="700pt"|Title<br />
|width="30pt"|Link to the paper<br />
|width="30pt"|Link to the summary<br />
|width="30pt"|Link to the video<br />
|-<br />
|-<br />
|Sep 15 (example)||Ri Wang || ||Sequence to sequence learning with neural networks.||[http://papers.nips.cc/paper/5346-sequence-to-sequence-learning-with-neural-networks.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Going_Deeper_with_Convolutions Summary] || [https://youtu.be/JWozRg_X-Vg?list=PLehuLRPyt1HzXDemu7K4ETcF0Ld_B5adG&t=539]<br />
|-<br />
|Week of Nov 2 || Jose Avilez || 1|| Gradientless Descent: High-Dimensional Zeroth-Order Optimisation || [https://openreview.net/pdf?id=Skep6TVYDB] || ||<br />
|-<br />
|Week of Nov 2 || Abhinav Chanana || 2||AUGMIX: A Simple Data Procession method to Improve Robustness And Uncertainity || [https://openreview.net/pdf?id=S1gmrxHFvB Paper] || ||<br />
|-<br />
|Week of Nov 2 || Maziar Dadbin || 3|| ALBERT: A Lite BERT for Self-supervised Learning of Language Representations || https://openreview.net/pdf?id=H1eA7AEtvS || ||<br />
|-<br />
|Week of Nov 2 ||John Edwards || 4||Learn, Imagine and Create: Text-to-Image Generation from Prior Knowledge ||[https://papers.nips.cc/paper/8375-learn-imagine-and-create-text-to-image-generation-from-prior-knowledge.pdf Paper] || ||<br />
|-<br />
|Week of Nov 2 ||Wenyu Shen || 5|| STRUCTBERT:INCORPORATING LANGUAGE STRUCTURES INTO PRETRAINING FOR DEEP LANGUAGE UNDERSTANDING || [https://openreview.net/pdf?id=BJgQ4lSFPH] || ||<br />
|-<br />
|Week of Nov 2 || Syed Saad Naseem || 6|| Learning The Difference That Makes A Difference With Counterfactually-Augmented Data|| [https://openreview.net/pdf?id=Sklgs0NFvr Paper] || ||<br />
|-<br />
|Week of Nov 9 || Donya Hamzeian || 7|| The Curious Case of Neural Text Degeneration || https://iclr.cc/virtual_2020/poster_rygGQyrFvH.html || ||<br />
|-<br />
|Week of Nov 9 || Parsa Torabian || 8|| Orthogonal Gradient Descent for Continual Learning || [http://proceedings.mlr.press/v108/farajtabar20a/farajtabar20a.pdf Paper] || ||<br />
|-<br />
|Week of Nov 9 || Arash Moayyedi || 9|| When Does Self-supervision Improve Few-shot Learning? || [https://openreview.net/forum?id=HkenPn4KPH Paper] || ||<br />
|-<br />
|Week of Nov 9 || Parsa Ashrafi Fashi || 10|| Probabilistic Model-Agnostic Meta-Learning || [http://papers.nips.cc/paper/8161-probabilistic-model-agnostic-meta-learning.pdf Paper] || ||<br />
|-<br />
|Week of Nov 9 || Jaskirat Singh Bhatia || 11|| A FAIRCOMPARISON OFGRAPHNEURALNETWORKSFORGRAPHCLASSIFICATION || [https://openreview.net/pdf?id=HygDF6NFPB Paper] || ||<br />
|-<br />
|Week of Nov 9 || Gaurav Sikri || 12|| EMPIRICAL STUDIES ON THE PROPERTIES OF LINEAR REGIONS IN DEEP NEURAL NETWORKS || [https://openreview.net/pdf?id=SkeFl1HKwr Paper] || ||<br />
|-<br />
|Week of Nov 16 || Abhinav Jain || 13|| The Logical Expressiveness of Graph Neural Networks || [http://www.openreview.net/pdf?id=r1lZ7AEKvB Paper] || ||<br />
|-<br />
|Week of Nov 16 || Gautam Bathla || 14|| One-Shot Object Detection with Co-Attention and Co-Excitation || [https://papers.nips.cc/paper/8540-one-shot-object-detection-with-co-attention-and-co-excitation.pdf Paper] || ||<br />
|-<br />
|Week of Nov 16 || Shikhar Sakhuja || 15|| SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems || [https://papers.nips.cc/paper/8589-superglue-a-stickier-benchmark-for-general-purpose-language-understanding-systems.pdf Paper] || ||<br />
|-<br />
|Week of Nov 16 || Cameron Meaney || 16|| Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations || [https://www.sciencedirect.com/science/article/pii/S0021999118307125 Paper] || ||<br />
|-<br />
|Week of Nov 16 ||Sobhan Hemati|| 17||Adversarial Fisher Vectors for Unsupervised Representation Learning||[https://papers.nips.cc/paper/9295-adversarial-fisher-vectors-for-unsupervised-representation-learning.pdf Paper]|| ||<br />
|-<br />
|Week of Nov 16 ||Milad Sikaroudi|| 18||Domain Genralization via Model Agnostic Learning of Semantic Features||[https://papers.nips.cc/paper/8873-domain-generalization-via-model-agnostic-learning-of-semantic-features.pdf Paper]|| ||<br />
|-<br />
|Week of Nov 23 ||Bowen You|| 19||DREAM TO CONTROL: LEARNING BEHAVIORS BY LATENT IMAGINATION||[https://openreview.net/pdf?id=S1lOTC4tDS Paper]|| ||<br />
|-<br />
|Week of Nov 23 ||Nouha Chatti|| 20|| This Looks Like That: Deep Learning for Interpretable Image Recognition||[https://papers.nips.cc/paper/9095-this-looks-like-that-deep-learning-for-interpretable-image-recognition.pdf Paper]|| ||<br />
|-<br />
|Week of Nov 23 || Mohan Wu || 21|| Pretrained Generalized Autoregressive Model with Adaptive Probabilistic Label Cluster for Extreme Multi-label Text Classification || [https://proceedings.icml.cc/static/paper_files/icml/2020/807-Paper.pdf Paper] || ||<br />
|-<br />
|Week of Nov 23 || Xinyi Yan || 22|| Incorporating BERT into Neural Machine Translation || [https://iclr.cc/virtual_2020/poster_Hyl7ygStwB.html Paper] || ||<br />
|-<br />
|Week of Nov 23 || Meixi Chen || 23|| Functional Regularisation for Continual Learning with Gaussian Processes || [https://arxiv.org/pdf/1901.11356.pdf Paper] || ||<br />
|-<br />
|Week of Nov 23 || Ahmed Salamah || 24|| Sparse Convolutional Neural Networks || [https://www.cv-foundation.org/openaccess/content_cvpr_2015/papers/Liu_Sparse_Convolutional_Neural_2015_CVPR_paper.pdf Paper] || ||<br />
|-<br />
|Week of Nov 23|| Mohammad Mahmoud || 32||Electrocardiogram heartbeat classification based on a deep convolutional neural network and focal loss|| [https://www.sciencedirect.com/science/article/abs/pii/S0010482520302237] || |-<br />
|-<br />
|Week of Nov 30 ||Danial Maleki || 25||Attention Is All You Need ||[https://arxiv.org/abs/1706.03762 Paper] || ||<br />
|-<br />
|Week of Nov 30 ||Gursimran Singh || 26||BERTScore: Evaluating Text Generation with BERT. ||[https://openreview.net/pdf?id=SkeHuCVFDr Paper] || ||<br />
|-<br />
|Week of Nov 30 || Govind Sharma || 27|| Time-series Generative Adversarial Networks || [https://papers.nips.cc/paper/8789-time-series-generative-adversarial-networks.pdf Paper] || ||<br />
|-<br />
|Week of Nov 30 ||Maral Rasoolijaberi|| 28||Parameter-free, Dynamic, and Strongly-Adaptive Online Learning|| [https://proceedings.icml.cc/static/paper_files/icml/2020/2820-Paper.pdf Paper] || ||<br />
|-<br />
|Week of Nov 30 || Sina Farsangi || 29|| Boosting Few-Shot Visual Learning with Self-Supervision || https://openaccess.thecvf.com/content_ICCV_2019/papers/Gidaris_Boosting_Few-Shot_Visual_Learning_With_Self-Supervision_ICCV_2019_paper.pdf || ||<br />
|-<br />
|Week of Nov 30 || Pierre McWhannel || 30|| Pre-training Tasks for Embedding-based Large-scale Retrieval || [https://openreview.net/pdf?id=rkg-mA4FDr Paper] || placeholder||<br />
|-<br />
|Week of Nov 30 || Wenjuan Qi || 31|| Network Deconvolution || [https://openreview.net/pdf?id=rkeu30EtvS Paper] || placeholder||</div>Mhamdyhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat940F21&diff=42838stat940F212020-10-26T19:40:06Z<p>Mhamdy: </p>
<hr />
<div>== [[F20-STAT 946-Proposal| Project Proposal ]] ==<br />
<br />
<br />
= Record your contributions here [https://docs.google.com/spreadsheets/d/1Me_O000pNxeTwNGEac57XakecG1wahvwGE5n36DGIlM/edit?usp=sharing]=<br />
<br />
Use the following notations:<br />
<br />
P: You have written a summary/critique on the paper.<br />
<br />
T: You had a technical contribution on a paper (excluding the paper that you present).<br />
<br />
E: You had an editorial contribution on a paper (excluding the paper that you present).<br />
<br />
<br />
=Paper presentation=<br />
{| class="wikitable"<br />
<br />
{| border="1" cellpadding="3"<br />
|-<br />
|width="60pt"|Date<br />
|width="100pt"|Name <br />
|width="30pt"|Paper number <br />
|width="700pt"|Title<br />
|width="30pt"|Link to the paper<br />
|width="30pt"|Link to the summary<br />
|width="30pt"|Link to the video<br />
|-<br />
|-<br />
|Sep 15 (example)||Ri Wang || ||Sequence to sequence learning with neural networks.||[http://papers.nips.cc/paper/5346-sequence-to-sequence-learning-with-neural-networks.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Going_Deeper_with_Convolutions Summary] || [https://youtu.be/JWozRg_X-Vg?list=PLehuLRPyt1HzXDemu7K4ETcF0Ld_B5adG&t=539]<br />
|-<br />
|Week of Nov 2 || Jose Avilez || 1|| Gradientless Descent: High-Dimensional Zeroth-Order Optimisation || [https://openreview.net/pdf?id=Skep6TVYDB] || ||<br />
|-<br />
|Week of Nov 2 || Abhinav Chanana || 2||AUGMIX: A Simple Data Procession method to Improve Robustness And Uncertainity || [https://openreview.net/pdf?id=S1gmrxHFvB Paper] || ||<br />
|-<br />
|Week of Nov 2 || Maziar Dadbin || 3|| ALBERT: A Lite BERT for Self-supervised Learning of Language Representations || https://openreview.net/pdf?id=H1eA7AEtvS || ||<br />
|-<br />
|Week of Nov 2 ||John Edwards || 4||Learn, Imagine and Create: Text-to-Image Generation from Prior Knowledge ||[https://papers.nips.cc/paper/8375-learn-imagine-and-create-text-to-image-generation-from-prior-knowledge.pdf Paper] || ||<br />
|-<br />
|Week of Nov 2 ||Wenyu Shen || 5|| STRUCTBERT:INCORPORATING LANGUAGE STRUCTURES INTO PRETRAINING FOR DEEP LANGUAGE UNDERSTANDING || [https://openreview.net/pdf?id=BJgQ4lSFPH] || ||<br />
|-<br />
|Week of Nov 2 || Syed Saad Naseem || 6|| Learning The Difference That Makes A Difference With Counterfactually-Augmented Data|| [https://openreview.net/pdf?id=Sklgs0NFvr Paper] || ||<br />
|-<br />
|Week of Nov 9 || Donya Hamzeian || 7|| The Curious Case of Neural Text Degeneration || https://iclr.cc/virtual_2020/poster_rygGQyrFvH.html || ||<br />
|-<br />
|Week of Nov 9 || Parsa Torabian || 8|| Orthogonal Gradient Descent for Continual Learning || [http://proceedings.mlr.press/v108/farajtabar20a/farajtabar20a.pdf Paper] || ||<br />
|-<br />
|Week of Nov 9 || Arash Moayyedi || 9|| When Does Self-supervision Improve Few-shot Learning? || [https://openreview.net/forum?id=HkenPn4KPH Paper] || ||<br />
|-<br />
|Week of Nov 9 || Parsa Ashrafi Fashi || 10|| Probabilistic Model-Agnostic Meta-Learning || [http://papers.nips.cc/paper/8161-probabilistic-model-agnostic-meta-learning.pdf Paper] || ||<br />
|-<br />
|Week of Nov 9 || Jaskirat Singh Bhatia || 11|| A FAIRCOMPARISON OFGRAPHNEURALNETWORKSFORGRAPHCLASSIFICATION || [https://openreview.net/pdf?id=HygDF6NFPB Paper] || ||<br />
|-<br />
|Week of Nov 9 || Gaurav Sikri || 12|| EMPIRICAL STUDIES ON THE PROPERTIES OF LINEAR REGIONS IN DEEP NEURAL NETWORKS || [https://openreview.net/pdf?id=SkeFl1HKwr Paper] || ||<br />
|-<br />
|Week of Nov 16 || Abhinav Jain || 13|| The Logical Expressiveness of Graph Neural Networks || [http://www.openreview.net/pdf?id=r1lZ7AEKvB Paper] || ||<br />
|-<br />
|Week of Nov 16 || Gautam Bathla || 14|| One-Shot Object Detection with Co-Attention and Co-Excitation || [https://papers.nips.cc/paper/8540-one-shot-object-detection-with-co-attention-and-co-excitation.pdf Paper] || ||<br />
|-<br />
|Week of Nov 16 || Shikhar Sakhuja || 15|| SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems || [https://papers.nips.cc/paper/8589-superglue-a-stickier-benchmark-for-general-purpose-language-understanding-systems.pdf Paper] || ||<br />
|-<br />
|Week of Nov 16 || Cameron Meaney || 16|| Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations || [https://www.sciencedirect.com/science/article/pii/S0021999118307125 Paper] || ||<br />
|-<br />
|Week of Nov 16 ||Sobhan Hemati|| 17||Adversarial Fisher Vectors for Unsupervised Representation Learning||[https://papers.nips.cc/paper/9295-adversarial-fisher-vectors-for-unsupervised-representation-learning.pdf Paper]|| ||<br />
|-<br />
|Week of Nov 16 ||Milad Sikaroudi|| 18||Domain Genralization via Model Agnostic Learning of Semantic Features||[https://papers.nips.cc/paper/8873-domain-generalization-via-model-agnostic-learning-of-semantic-features.pdf Paper]|| ||<br />
|-<br />
|Week of Nov 23 ||Bowen You|| 19||DREAM TO CONTROL: LEARNING BEHAVIORS BY LATENT IMAGINATION||[https://openreview.net/pdf?id=S1lOTC4tDS Paper]|| ||<br />
|-<br />
|Week of Nov 23 ||Nouha Chatti|| 20|| This Looks Like That: Deep Learning for Interpretable Image Recognition||[https://papers.nips.cc/paper/9095-this-looks-like-that-deep-learning-for-interpretable-image-recognition.pdf Paper]|| ||<br />
|-<br />
|Week of Nov 23 || Mohan Wu || 21|| Pretrained Generalized Autoregressive Model with Adaptive Probabilistic Label Cluster for Extreme Multi-label Text Classification || [https://proceedings.icml.cc/static/paper_files/icml/2020/807-Paper.pdf Paper] || ||<br />
|-<br />
|Week of Nov 23 || Xinyi Yan || 22|| Incorporating BERT into Neural Machine Translation || [https://iclr.cc/virtual_2020/poster_Hyl7ygStwB.html Paper] || ||<br />
|-<br />
|Week of Nov 23 || Meixi Chen || 23|| Functional Regularisation for Continual Learning with Gaussian Processes || [https://arxiv.org/pdf/1901.11356.pdf Paper] || ||<br />
|-<br />
|Week of Nov 23 || Ahmed Salamah || 24|| Sparse Convolutional Neural Networks || [https://www.cv-foundation.org/openaccess/content_cvpr_2015/papers/Liu_Sparse_Convolutional_Neural_2015_CVPR_paper.pdf Paper] || ||<br />
|-<br />
|Week of Nov 30 ||Danial Maleki || 25||Attention Is All You Need ||[https://arxiv.org/abs/1706.03762 Paper] || ||<br />
|-<br />
|Week of Nov 30 ||Gursimran Singh || 26||BERTScore: Evaluating Text Generation with BERT. ||[https://openreview.net/pdf?id=SkeHuCVFDr Paper] || ||<br />
|-<br />
|Week of Nov 30 || Govind Sharma || 27|| Time-series Generative Adversarial Networks || [https://papers.nips.cc/paper/8789-time-series-generative-adversarial-networks.pdf Paper] || ||<br />
|-<br />
|Week of Nov 30 ||Maral Rasoolijaberi|| 28||Parameter-free, Dynamic, and Strongly-Adaptive Online Learning|| [https://proceedings.icml.cc/static/paper_files/icml/2020/2820-Paper.pdf Paper] || ||<br />
|-<br />
|Week of Nov 30 || Sina Farsangi || 29|| Boosting Few-Shot Visual Learning with Self-Supervision || https://openaccess.thecvf.com/content_ICCV_2019/papers/Gidaris_Boosting_Few-Shot_Visual_Learning_With_Self-Supervision_ICCV_2019_paper.pdf || ||<br />
|-<br />
|Week of Nov 30 || Pierre McWhannel || 30|| Pre-training Tasks for Embedding-based Large-scale Retrieval || [https://openreview.net/pdf?id=rkg-mA4FDr Paper] || placeholder||<br />
|-<br />
|Week of Nov 30 || Wenjuan Qi || 31|| Network Deconvolution || [https://openreview.net/pdf?id=rkeu30EtvS Paper] || placeholder||<br />
|-<br />
|Week of Nov 30|| Mohammad Mahmoud || 32||Electrocardiogram heartbeat classification based on a deep convolutional neural network and focal loss|| [https://www.sciencedirect.com/science/article/abs/pii/S0010482520302237] || |-</div>Mhamdyhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat940F21&diff=42837stat940F212020-10-26T19:39:41Z<p>Mhamdy: </p>
<hr />
<div>== [[F20-STAT 946-Proposal| Project Proposal ]] ==<br />
<br />
<br />
= Record your contributions here [https://docs.google.com/spreadsheets/d/1Me_O000pNxeTwNGEac57XakecG1wahvwGE5n36DGIlM/edit?usp=sharing]=<br />
<br />
Use the following notations:<br />
<br />
P: You have written a summary/critique on the paper.<br />
<br />
T: You had a technical contribution on a paper (excluding the paper that you present).<br />
<br />
E: You had an editorial contribution on a paper (excluding the paper that you present).<br />
<br />
<br />
=Paper presentation=<br />
{| class="wikitable"<br />
<br />
{| border="1" cellpadding="3"<br />
|-<br />
|width="60pt"|Date<br />
|width="100pt"|Name <br />
|width="30pt"|Paper number <br />
|width="700pt"|Title<br />
|width="30pt"|Link to the paper<br />
|width="30pt"|Link to the summary<br />
|width="30pt"|Link to the video<br />
|-<br />
|-<br />
|Sep 15 (example)||Ri Wang || ||Sequence to sequence learning with neural networks.||[http://papers.nips.cc/paper/5346-sequence-to-sequence-learning-with-neural-networks.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Going_Deeper_with_Convolutions Summary] || [https://youtu.be/JWozRg_X-Vg?list=PLehuLRPyt1HzXDemu7K4ETcF0Ld_B5adG&t=539]<br />
|-<br />
|Week of Nov 2 || Jose Avilez || 1|| Gradientless Descent: High-Dimensional Zeroth-Order Optimisation || [https://openreview.net/pdf?id=Skep6TVYDB] || ||<br />
|-<br />
|Week of Nov 2 || Abhinav Chanana || 2||AUGMIX: A Simple Data Procession method to Improve Robustness And Uncertainity || [https://openreview.net/pdf?id=S1gmrxHFvB Paper] || ||<br />
|-<br />
|Week of Nov 2 || Maziar Dadbin || 3|| ALBERT: A Lite BERT for Self-supervised Learning of Language Representations || https://openreview.net/pdf?id=H1eA7AEtvS || ||<br />
|-<br />
|Week of Nov 2 ||John Edwards || 4||Learn, Imagine and Create: Text-to-Image Generation from Prior Knowledge ||[https://papers.nips.cc/paper/8375-learn-imagine-and-create-text-to-image-generation-from-prior-knowledge.pdf Paper] || ||<br />
|-<br />
|Week of Nov 2 ||Wenyu Shen || 5|| STRUCTBERT:INCORPORATING LANGUAGE STRUCTURES INTO PRETRAINING FOR DEEP LANGUAGE UNDERSTANDING || [https://openreview.net/pdf?id=BJgQ4lSFPH] || ||<br />
|-<br />
|Week of Nov 2 || Syed Saad Naseem || 6|| Learning The Difference That Makes A Difference With Counterfactually-Augmented Data|| [https://openreview.net/pdf?id=Sklgs0NFvr Paper] || ||<br />
|-<br />
|Week of Nov 9 || Donya Hamzeian || 7|| The Curious Case of Neural Text Degeneration || https://iclr.cc/virtual_2020/poster_rygGQyrFvH.html || ||<br />
|-<br />
|Week of Nov 9 || Parsa Torabian || 8|| Orthogonal Gradient Descent for Continual Learning || [http://proceedings.mlr.press/v108/farajtabar20a/farajtabar20a.pdf Paper] || ||<br />
|-<br />
|Week of Nov 9 || Arash Moayyedi || 9|| When Does Self-supervision Improve Few-shot Learning? || [https://openreview.net/forum?id=HkenPn4KPH Paper] || ||<br />
|-<br />
|Week of Nov 9 || Parsa Ashrafi Fashi || 10|| Probabilistic Model-Agnostic Meta-Learning || [http://papers.nips.cc/paper/8161-probabilistic-model-agnostic-meta-learning.pdf Paper] || ||<br />
|-<br />
|Week of Nov 9 || Jaskirat Singh Bhatia || 11|| A FAIRCOMPARISON OFGRAPHNEURALNETWORKSFORGRAPHCLASSIFICATION || [https://openreview.net/pdf?id=HygDF6NFPB Paper] || ||<br />
|-<br />
|Week of Nov 9 || Gaurav Sikri || 12|| EMPIRICAL STUDIES ON THE PROPERTIES OF LINEAR REGIONS IN DEEP NEURAL NETWORKS || [https://openreview.net/pdf?id=SkeFl1HKwr Paper] || ||<br />
|-<br />
|Week of Nov 16 || Abhinav Jain || 13|| The Logical Expressiveness of Graph Neural Networks || [http://www.openreview.net/pdf?id=r1lZ7AEKvB Paper] || ||<br />
|-<br />
|Week of Nov 16 || Gautam Bathla || 14|| One-Shot Object Detection with Co-Attention and Co-Excitation || [https://papers.nips.cc/paper/8540-one-shot-object-detection-with-co-attention-and-co-excitation.pdf Paper] || ||<br />
|-<br />
|Week of Nov 16 || Shikhar Sakhuja || 15|| SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems || [https://papers.nips.cc/paper/8589-superglue-a-stickier-benchmark-for-general-purpose-language-understanding-systems.pdf Paper] || ||<br />
|-<br />
|Week of Nov 16 || Cameron Meaney || 16|| Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations || [https://www.sciencedirect.com/science/article/pii/S0021999118307125 Paper] || ||<br />
|-<br />
|Week of Nov 16 ||Sobhan Hemati|| 17||Adversarial Fisher Vectors for Unsupervised Representation Learning||[https://papers.nips.cc/paper/9295-adversarial-fisher-vectors-for-unsupervised-representation-learning.pdf Paper]|| ||<br />
|-<br />
|Week of Nov 16 ||Milad Sikaroudi|| 18||Domain Genralization via Model Agnostic Learning of Semantic Features||[https://papers.nips.cc/paper/8873-domain-generalization-via-model-agnostic-learning-of-semantic-features.pdf Paper]|| ||<br />
|-<br />
|Week of Nov 23 ||Bowen You|| 19||DREAM TO CONTROL: LEARNING BEHAVIORS BY LATENT IMAGINATION||[https://openreview.net/pdf?id=S1lOTC4tDS Paper]|| ||<br />
|-<br />
|Week of Nov 23 ||Nouha Chatti|| 20|| This Looks Like That: Deep Learning for Interpretable Image Recognition||[https://papers.nips.cc/paper/9095-this-looks-like-that-deep-learning-for-interpretable-image-recognition.pdf Paper]|| ||<br />
|-<br />
|Week of Nov 23 || Mohan Wu || 21|| Pretrained Generalized Autoregressive Model with Adaptive Probabilistic Label Cluster for Extreme Multi-label Text Classification || [https://proceedings.icml.cc/static/paper_files/icml/2020/807-Paper.pdf Paper] || ||<br />
|-<br />
|Week of Nov 23 || Xinyi Yan || 22|| Incorporating BERT into Neural Machine Translation || [https://iclr.cc/virtual_2020/poster_Hyl7ygStwB.html Paper] || ||<br />
|-<br />
|Week of Nov 23 || Meixi Chen || 23|| Functional Regularisation for Continual Learning with Gaussian Processes || [https://arxiv.org/pdf/1901.11356.pdf Paper] || ||<br />
|-<br />
|Week of Nov 23 || Ahmed Salamah || 24|| Sparse Convolutional Neural Networks || [https://www.cv-foundation.org/openaccess/content_cvpr_2015/papers/Liu_Sparse_Convolutional_Neural_2015_CVPR_paper.pdf Paper] || ||<br />
|-<br />
|Week of Nov 30 ||Danial Maleki || 25||Attention Is All You Need ||[https://arxiv.org/abs/1706.03762 Paper] || ||<br />
|-<br />
|Week of Nov 30 ||Gursimran Singh || 26||BERTScore: Evaluating Text Generation with BERT. ||[https://openreview.net/pdf?id=SkeHuCVFDr Paper] || ||<br />
|-<br />
|Week of Nov 30 || Govind Sharma || 27|| Time-series Generative Adversarial Networks || [https://papers.nips.cc/paper/8789-time-series-generative-adversarial-networks.pdf Paper] || ||<br />
|-<br />
|Week of Nov 30 ||Maral Rasoolijaberi|| 28||Parameter-free, Dynamic, and Strongly-Adaptive Online Learning|| [https://proceedings.icml.cc/static/paper_files/icml/2020/2820-Paper.pdf Paper] || ||<br />
|-<br />
|Week of Nov 30 || Sina Farsangi || 29|| Boosting Few-Shot Visual Learning with Self-Supervision || https://openaccess.thecvf.com/content_ICCV_2019/papers/Gidaris_Boosting_Few-Shot_Visual_Learning_With_Self-Supervision_ICCV_2019_paper.pdf || ||<br />
|-<br />
|Week of Nov 30 || Pierre McWhannel || 30|| Pre-training Tasks for Embedding-based Large-scale Retrieval || [https://openreview.net/pdf?id=rkg-mA4FDr Paper] || placeholder||<br />
|-<br />
|Week of Nov 30 || Wenjuan Qi || 31|| Network Deconvolution || [https://openreview.net/pdf?id=rkeu30EtvS Paper] || placeholder||<br />
|-<br />
|Week of Nov 30|| Mohammad Mahmoud || 31||Electrocardiogram heartbeat classification based on a deep convolutional neural network and focal loss|| [https://www.sciencedirect.com/science/article/abs/pii/S0010482520302237] || |-</div>Mhamdy