Difference between revisions of "CatBoost: unbiased boosting with categorical features"

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== Introduction ==  
 
== Introduction ==  
This paper presents a deep convolutional neural network architecture codenamed Inception. This newly designed architecture enhances the utilization of the computing resources by increasing the depth and width of the network, while maintaining the computational budget constraint. DNNs are powerful because they can perform arbitrary parallel computation for a modest number of steps. The proposed architecture was implemented through a 22 layers deep network called GoogLeNet and significantly outperformed the state of the art in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC14).
+
This paper presents a new boosting strategy: CatBoost with the key techniques of the algorithm. It is a new gradient boosting method and it outperforms other publicly available boosting methods in practice. The implementation of ordered boosting and the innovative way for processing categorical features  are the two algorithmic advance introduced in CatBoost. It can deal with the prediction shift problem which is being discussed in details. In this paper, the authors provide the theoretical derivation of the algorithm along with the intuitive examples to demonstrate the strength and the efficiency of the model.
  
 
== Previous Work ==  
 
== Previous Work ==  
  
The current architecture is built on the network-in-network approach proposed by Lin et al.[1] for the purpose of increase the representation power of the neural networks. They added additional 1 X 1 convolutional layers, serving as dimension reduction modules to significantly reduce the number of parameters of the model. The paper also took inspiration from the Regions with Convolutional Neural Networks (R-CNN) proposed by Girshick et al. [2]. The overall detection problem is divided into two subproblems:  
+
The CatBoost algorithm is new algorithm based on the gradient boosting method, which is a powerful machine-learning techniques with solid theoretical basis and strong predicting power. This new algorithm is built for the purpose of dealing with the prediction shift problem, which was discussed before in the paper [3,13] on boosting without a formal definition. This paper proposed this new algorithm and presented the analysis on how the existing problem is solved by this new algorithm. The previous work in paper [1,15,18,22] inspired the authors to propose a new algorithm to deal with categorical features. Here are the two main aspects considered in this new algorithm:
  
1. Utilize low-level cues for potential object proposals
+
1. Ordered boosting, a modification of standard gradient boosting algorithm 
  
2. Classify object categories with CNN
+
2. Categorical features, a new algorithm for processing categorical features
  
 
== Motivation ==  
 
== Motivation ==  
Line 17: Line 17:
 
Gradient boosting is known to be a popular and powerful machine learning method that could potentially increase the accuracy of a model. It aims to identify strong predictors in a model by performing gradient descent. Nevertheless, there exists a statistical issue which makes gradient boosting less powerful as we intended it to be. The paper identified this issue as prediction shift caused by target leakage.
 
Gradient boosting is known to be a popular and powerful machine learning method that could potentially increase the accuracy of a model. It aims to identify strong predictors in a model by performing gradient descent. Nevertheless, there exists a statistical issue which makes gradient boosting less powerful as we intended it to be. The paper identified this issue as prediction shift caused by target leakage.
  
A prediction shift happens when there is a shift between the predicted model trained on the training samples and the distribution of the test samples. This often occurs as the predicted model is trained using all training samples and not all training samples are fully representative of the test samples. In gradient boosting, the current estimate <math>F^t</math> is based on the previous model <math>F^{t-1}</math> we built on earlier in each iteration. To better demonstrate a prediction shift, it essentially means that <math>F^{t-1}(\bf{x_k})|\bf{x_k}</math> where <math>\bf{x_k}</math> comes from training samples is shifted from <math>F^{t-1}(\bf{x})|\bf{x}</math> where <math>\bf{x}</math> comes from testing samples. This is caused by target leakage where the distribution of the estimated model is different from the distribution of the testing samples. To identify this issue, we will introduce ''ordered boosting'' which is the motivation behind categorical boosting.
+
A prediction shift happens when there is a shift between the predicted model trained on the training samples and the distribution of the test samples. This often occurs as the predicted model is trained using all training samples and not all training samples are fully representative of the test samples. When the predicted model is trained using all training samples, it could lead to a biased model since the model has seen the labels during its learning stage. In gradient boosting, the current estimate <math>F^t</math> is based on the previous model <math>F^{t-1}</math> we built on earlier in each iteration. To better demonstrate a prediction shift, it essentially means that <math>F^{t-1}(\bf{x_k})|\bf{x_k}</math> where <math>\bf{x_k}</math> comes from training samples is shifted from <math>F^{t-1}(\bf{x})|\bf{x}</math> where <math>\bf{x}</math> comes from testing samples. This is caused by target leakage where the distribution of the estimated model is different from the distribution of the testing samples. Therefore, the model is biased and could lead to overfitting in some cases. To identify this issue, we will introduce ''ordered boosting'' which is the motivation behind categorical boosting.
  
  
== Ordered Boosting ==  
+
== Ordered Target Statistics ==
The Inception architecture consists of stacking blocks called the inception modules. The idea is that to increase the depth and width of model by finding local optimal sparse structure and repeating it spatially. Traditionally, in each layer of convolutional network pooling operation and convolution and its size (1 by 1, 3 by 3 or 5 by 5) should be decided while all of them are beneficial for the modeling power of the network. Whereas, in Inception module instead of choosing, all these various options are computed simultaneously (Fig. 1a). Inspired by layer-by-layer construction of Arora et al. [3], in Inception module statistics correlation of the last layer is analyzed and clustered into groups of units with high correlation. These clusters form units of next layer and are connected to the units of previous layer. Each unit from the earlier layer corresponds to some region of the input image and the outputs of them are concatenated into a filter bank. Additionally, because of the beneficial effect of pooling in the convolutional networks, a parallel path of pooling has been added in each module. The Inception module in its naïve form (Fig. 1a) suffers from high computation and power cost. In addition, as the concatenated output from the various convolutions and the pooling layer will be an extremely deep channel of output volume, the claim that this architecture has an improved memory and computation power use looks like counterintuitive. However, this issue has been addressed by adding a 1 by 1 convolution before costly 3 by 3 and 5 by 5 convolutions. The idea of 1 by 1 convolution was first introduced by Lin et al. and called network in network [1]. This 1x1 convolution mathematically is equivalent to a multilayer perceptron which reduces the dimension of filter space (the depth of the output volume) and on top of that they also act as a non-linear rectifying activation layer ReLu to add to the non-linearity immediately after each 1 by 1 convolution (Fig. 1b). This enables less over-fitting due to smaller Kernel size (1 by 1). This distinctive dimensionality reduction feature of the 1 by 1 convolution allows shielding of the large number of input filters of the previous stage to the next stage (Footnote 2).
 
  
[[File:Inception module, naıve version.JPG | center]]
+
Before the introduction of ordered boosting, we will first introduce the concept of ordered target statistics. The reason why ordered target statistics is used in this algorithm is to avoid overfitting. In ordered target statistics, a random permutation on the training samples is constructed so that we train our model based on the new training samples in which our current model has never seen previously. Define a target statistic as <math>\hat{x}_k^i = E(y | x^i = x_k^i)</math> where <math>k</math> refers to <math>k^{th}</math> training samples and <math>i</math> refers to <math>i^{th}</math> categorical feature.
  
<div align="center">Figure 1(a): Inception module, naïve version</div>
+
In ordered target statistics, a random permutation <math>\sigma</math> is generated to help the algorithm to obtain training samples sequentially. For instance, if we would like to obtain <math>k^{th}</math> training samples, then <math>D_k = {x_j : \sigma(j)<\sigma(k)}</math>. Through this method, we can ensure that the model is unbiased as the trained model is obtained based on the new samples in which the model has never seen. In the traditional boosting method, the model is obtained based on all the training samples which could possibly lead to overfitting as we train the model based on what the model has seen previously. Therefore, the issue of overfitting motivates the idea of ordered target statistics which we will use to generate the permutations of our training samples.
  
[[File:Inception module with dimension reductions.JPG | center]]
+
== Ordered Boosting ==
  
<div align="center">Figure 1(b): Inception module with dimension reductions</div>
+
To overcome the prediction shift discussed in the previous section, ''ordered boosting'' is introduced. In ordered boosting, a new training dataset is obtained in each step of boosting. This means that the model is trained such that the model we obtained previously is applied to this set of new training samples. This guarantees that the model in which we have obtained previously has not seen the labels in the new training set. Therefore, the trained model at each step of boosting is not biased. To better illustrate this, assuming <math>M_t</math> is our current model in <math>{t+1}^{th}</math> iteration which is learned using only the first t samples, the residual <math>r^{t+1} = y_i - M_{t}</math> is unshifted since the model is trained without the observations in the new training set. This is supported by the generation of random permutations <math>\sigma</math> of our training samples. To illustrate this idea, please see Figure (1).
+
[[File:Ordered boosting principle.png | center]]
The combination of various layers of convolution has some similarity with human eyes in interpreting the visual information in a sense that human eyes also process the visual information at various scale and combines to extract the features from different scale simultaneously. Similarly, in inception design network in network designs extract the fine grain details of input volume while medium- and large-sized filters cover a large receptive field of the inputs and extract their features and with pooling operations overfitting can be overcome by reducing the spatial sizes.
+
<div align="center">Figure 1: Ordered boosting principle, ordered by <math>\sigma</math></div>
  
== ILSVRC 2014 Challenge Results ==
+
In ordered boosting, the algorithm starts with generating <math>s+1</math> independent random permutations <math>\sigma_0, \sigma_1, \dots, \sigma_s</math> of the training dataset. <math>\sigma_1, \dots, \sigma_s</math> contributes to the internal nodes of a tree where the evaluation of the splits takes place. <math>\sigma_0</math> contributes to the terminal nodes where the leaf value is determined. the algorithm starts with building a decision tree based on the base predictors. The same splitting criterion is used in building a decision tree in the context of ordered boosting. Note that the trees built under this model are symmetric as this helps to improvise the algorithm in terms of its runtime.  
The proposed architecture was implemented through a deep network called GoogLeNet as a submission for ILSVRC14’s Classification Challenge and Detection Challenge.  
 
  
The classification challenge is to classify images into one of 1000 categories in the Imagenet hierarchy. The top-5 error rate -  the percentage of test examples for which the correct class is not in the top 5 predicted classes - is used for measuring accuracy. The results of the classification challenge is shown in Table 1. The final submission of GoogLeNet obtains a top-5 error of 6.67% on both the validation and testing data, ranking first among all participants, significantly outperforming top teams in previous years, and not utilizing external data.
+
Define <math>M_{r,j}(i)</math> as our current model for the ''i''-th sample based on the first ''j'' samples. A random permutation <math>\sigma_r</math> is sampled from the <math>s+1</math> independent random permutations of the training dataset. The random permutation, says <math>\sigma_r</math>, will then contribute to our construction of tree, <math>T_t</math>.  
  
[[File:Classification performance.JPG | center|500px|Image: 500 pixels]]
+
A gradient is computed at each step such that <math>grad_{r,j}(i)=\frac{\delta{L(y_i,M_{r,j}(i))}}{\delta{s}}</math>. The leaf value for the tree constructed based on the ''i''-th sample will then be equals to the average of the gradients computed, which can be written as:
 +
$$\text{avg } grad_{r, \sigma_r(i)-1}$$
 +
When a tree, <math>T_t</math> is constructed, the tree itself is used to boost all the existing models <math>M_{r',j}</math>. Finally, in our final model, <math>F</math>, the leaf values are computed using the standard gradient boosting procedure. Recall that <math>\sigma_0</math> is used to determine the final leaf values. Therefore, once we obtain our final model, we match the training samples, says <math>i^{th}</math> sample, to <math>leaf_0(i)</math> and so on. See Figure 2 for the detailed algorithm of how CatBoost build a decision tree.
 +
[[File:Catboost tree algorithm.png | center]]
 +
<div align="center">Figure 2: Algorithm to build a tree in Catboost</div>
  
<div align="center">Table 1: Classification performance</div>
 
  
The ILSVRC detection challenge asks to produce bounding boxes around objects in images among 200 classes. Detected objects count as correct if they match the class of the groundtruth and their bounding boxes overlap by at least 50%. Each image may contain multiple objects (with different scales) or none. The mean average precision (mAP) is used to report performance. The results of the detection challenge is listed in Table 2. Using the Inception model as a region classifier, combining Selective Search and using an ensemble of 6 CNNs, GoogLeNet gave top detection results, almost doubling accuracy of the the 2013 top model.
 
  
[[File:Detection performance.JPG | center|600px|Image: 600 pixels]]
 
  
<div align="center">Table 2: Detection performance</div>
+
== CatBoost Results ==
 +
CatBoost is implemented as an algorithm for gradient boosting on decision trees. The algorithm is compared with the most popular open-source libraries – XGBoost and LightBGM. Categorical features are preprocessed using Ordered TS method for CatBoost.  The results measured by logloss and zero-one loss are presented in Table 1. The statistical significance of performance is also presented in Table 1.
 +
 
 +
[[File:Table1.png | center|500px|Image: 500 pixels]]
 +
 
 +
<div align="center">Table 1: Comparison with baselines: logloss / zero-one loss (relative increase for baselines).</div>
 +
 
 +
Besides, the running time for CatBoost Plain and LightGBM are the fastest ones followed by Ordered mode, which is about 1.7 times slower.
 +
 
 +
Comparison between boosting modes of CatBoost: Plain and Ordered is performed on all considered datasets, and the results are presented in Table 2. It is evident that Ordered mode is especially effective on smaller datasets, which supports the hypothesis that a larger bias has a negative effect on performance.
 +
 
 +
[[File:Table2.png | center|600px|Image: 600 pixels]]
 +
 
 +
<div align="center">Table 2: Plain boosting mode: logloss, zeroone loss and their change relative to Ordered boosting mode.</div>
 +
 
 +
As illustrated in Figure 2, CatBoost is trained in Ordered and Plain modes on randomly filtered datasets to compare the generated losses. The relative performance of Plain modes becomes worse as the dataset size decreases. 
 +
 
 +
[[File:Figure2.png | center|500px|Image: 500 pixels]]
 +
 
 +
<div align="center">Figure 2: Relative error of Plain boosting mode compared to Ordered boosting mode depending on the fraction of the dataset. </div>
 +
 
 +
Different TSs options of CatBoost in Ordered boosting mode are being compared and the outcomes can be found in Table 3. Ordered TS used in CatBoost outscored all other approaches significantly. Among the baselines, the holdout TS is the best for a majority of the datasets. 
 +
 
 +
[[File:Table3.png | center|500px|Image: 500 pixels]]
 +
 
 +
<div align="center">Table 3: Comparison of target statistics, relative change in logloss / zero-one loss compared to ordered TS. </div>
  
 
== Conclusion ==
 
== Conclusion ==
Googlenet outperformed the other previous deep learning networks, and it became a proof of concept that approximating the expected optimal sparse structure by readily available dense building blocks (or the inception modules) is a viable method for improving the neural networks in computer vision. The significant quality gain is at a modest increase for the computational requirement is the main advantage for this method. Even without performing any bounding box operations to detect objects, this architecture gained a significant amount of quality with a modest amount of computational resources.
+
 
 +
CatBoost has two unique advancements: the implementation of ordered boosting and ordered TS to tackle the problem of prediction shift caused by target leakage present in all existing implementations of gradient boosting. The empirical result shows that CatBoost overperforms other GBDT packages on most of the datasets and thus CatBoost is an effective tool for use in supervised machine learning technique.  
  
 
== Critiques ==
 
== Critiques ==
By using nearly 5 million parameters, GoogLeNet, compared to previous architectures like VGGNet and AlexNet, reduced the number of parameters in the network by almost 92%. This enabled Inception to be used for many big data applications where a huge amount of data was needed to be processed at a reasonable cost while the computational capacity was limited. However, the Inception network is still complex and susceptible to scaling. If the network is scaled up, large parts of the computational gains can be lost immediately. Also, there was no clear description about the various factors that lead to the design decision of this inception architecture, making it harder to adapt to other applications while maintaining the same computational efficiency.
 
  
-
+
Strength
 +
 
 +
1) The proposed algorithm and current statistical issues are presented in a simple manner
 +
 
 +
2) Solid empirical study of the new algorithm compared to current methodologies such as XGBoost and lightGBM
 +
 
 +
 
 +
Weakness
 +
 
 +
1) This paper performs the experiment on heterogenous, categorical datasets. It does not show the performance of CatBoost relative to XGBoost and LightBoost when working with homogenous data. Hence, it may be biased to state that CatBoost outperforms other leading GBDT packages.
 +
 
 +
2) The tasks in the experiment are classification tasks. Author should include regression task to determine if the result holds for regression problem.
 +
 
 +
3) The hyper-parameter setting such as iteration, maximum tree depth and so on can impact CatBoost's performance relative to other GBDT implementation. CatBoost's Oblivious Decision Tree (ODT) are balanced by definition. The "maximum tree depth" will have an impact on the amount of memory and running time. Iteration specifies the maximum number of decision tree CatBoost will construct. It is possible that the author tune their hyperpararameter so that it looks better than for the baselines.
  
 
== References ==
 
== References ==
Line 92: Line 129:
 
[17] M. Kearns and L. Valiant. Cryptographic limitations on learning boolean formulae and finite automata. Journal of the ACM (JACM), 41(1):67–95, 1994.
 
[17] M. Kearns and L. Valiant. Cryptographic limitations on learning boolean formulae and finite automata. Journal of the ACM (JACM), 41(1):67–95, 1994.
  
[18] J. Langford, L. Li, and T. Zhang. Sparse online learning via truncated gradient. Journal of Machine Learning Research, 10(Mar):777–801, 2009. 10
+
[18] J. Langford, L. Li, and T. Zhang. Sparse online learning via truncated gradient. Journal of Machine Learning Research, 10(Mar):777–801, 2009.  
  
 
[19] LightGBM. Categorical feature support. http://lightgbm.readthedocs.io/en/latest/Advanced-Topics.html#categorical-feature-support, 2017.
 
[19] LightGBM. Categorical feature support. http://lightgbm.readthedocs.io/en/latest/Advanced-Topics.html#categorical-feature-support, 2017.

Latest revision as of 02:36, 23 November 2021

Presented by

Jessie Man Wai Chin, Yi Lin Ooi, Yaqi Shi, Shwen Lyng Ngew

Introduction

This paper presents a new boosting strategy: CatBoost with the key techniques of the algorithm. It is a new gradient boosting method and it outperforms other publicly available boosting methods in practice. The implementation of ordered boosting and the innovative way for processing categorical features are the two algorithmic advance introduced in CatBoost. It can deal with the prediction shift problem which is being discussed in details. In this paper, the authors provide the theoretical derivation of the algorithm along with the intuitive examples to demonstrate the strength and the efficiency of the model.

Previous Work

The CatBoost algorithm is new algorithm based on the gradient boosting method, which is a powerful machine-learning techniques with solid theoretical basis and strong predicting power. This new algorithm is built for the purpose of dealing with the prediction shift problem, which was discussed before in the paper [3,13] on boosting without a formal definition. This paper proposed this new algorithm and presented the analysis on how the existing problem is solved by this new algorithm. The previous work in paper [1,15,18,22] inspired the authors to propose a new algorithm to deal with categorical features. Here are the two main aspects considered in this new algorithm:

1. Ordered boosting, a modification of standard gradient boosting algorithm

2. Categorical features, a new algorithm for processing categorical features

Motivation

Gradient boosting is known to be a popular and powerful machine learning method that could potentially increase the accuracy of a model. It aims to identify strong predictors in a model by performing gradient descent. Nevertheless, there exists a statistical issue which makes gradient boosting less powerful as we intended it to be. The paper identified this issue as prediction shift caused by target leakage.

A prediction shift happens when there is a shift between the predicted model trained on the training samples and the distribution of the test samples. This often occurs as the predicted model is trained using all training samples and not all training samples are fully representative of the test samples. When the predicted model is trained using all training samples, it could lead to a biased model since the model has seen the labels during its learning stage. In gradient boosting, the current estimate [math]F^t[/math] is based on the previous model [math]F^{t-1}[/math] we built on earlier in each iteration. To better demonstrate a prediction shift, it essentially means that [math]F^{t-1}(\bf{x_k})|\bf{x_k}[/math] where [math]\bf{x_k}[/math] comes from training samples is shifted from [math]F^{t-1}(\bf{x})|\bf{x}[/math] where [math]\bf{x}[/math] comes from testing samples. This is caused by target leakage where the distribution of the estimated model is different from the distribution of the testing samples. Therefore, the model is biased and could lead to overfitting in some cases. To identify this issue, we will introduce ordered boosting which is the motivation behind categorical boosting.


Ordered Target Statistics

Before the introduction of ordered boosting, we will first introduce the concept of ordered target statistics. The reason why ordered target statistics is used in this algorithm is to avoid overfitting. In ordered target statistics, a random permutation on the training samples is constructed so that we train our model based on the new training samples in which our current model has never seen previously. Define a target statistic as [math]\hat{x}_k^i = E(y | x^i = x_k^i)[/math] where [math]k[/math] refers to [math]k^{th}[/math] training samples and [math]i[/math] refers to [math]i^{th}[/math] categorical feature.

In ordered target statistics, a random permutation [math]\sigma[/math] is generated to help the algorithm to obtain training samples sequentially. For instance, if we would like to obtain [math]k^{th}[/math] training samples, then [math]D_k = {x_j : \sigma(j)\lt \sigma(k)}[/math]. Through this method, we can ensure that the model is unbiased as the trained model is obtained based on the new samples in which the model has never seen. In the traditional boosting method, the model is obtained based on all the training samples which could possibly lead to overfitting as we train the model based on what the model has seen previously. Therefore, the issue of overfitting motivates the idea of ordered target statistics which we will use to generate the permutations of our training samples.

Ordered Boosting

To overcome the prediction shift discussed in the previous section, ordered boosting is introduced. In ordered boosting, a new training dataset is obtained in each step of boosting. This means that the model is trained such that the model we obtained previously is applied to this set of new training samples. This guarantees that the model in which we have obtained previously has not seen the labels in the new training set. Therefore, the trained model at each step of boosting is not biased. To better illustrate this, assuming [math]M_t[/math] is our current model in [math]{t+1}^{th}[/math] iteration which is learned using only the first t samples, the residual [math]r^{t+1} = y_i - M_{t}[/math] is unshifted since the model is trained without the observations in the new training set. This is supported by the generation of random permutations [math]\sigma[/math] of our training samples. To illustrate this idea, please see Figure (1).

Ordered boosting principle.png
Figure 1: Ordered boosting principle, ordered by [math]\sigma[/math]

In ordered boosting, the algorithm starts with generating [math]s+1[/math] independent random permutations [math]\sigma_0, \sigma_1, \dots, \sigma_s[/math] of the training dataset. [math]\sigma_1, \dots, \sigma_s[/math] contributes to the internal nodes of a tree where the evaluation of the splits takes place. [math]\sigma_0[/math] contributes to the terminal nodes where the leaf value is determined. the algorithm starts with building a decision tree based on the base predictors. The same splitting criterion is used in building a decision tree in the context of ordered boosting. Note that the trees built under this model are symmetric as this helps to improvise the algorithm in terms of its runtime.

Define [math]M_{r,j}(i)[/math] as our current model for the i-th sample based on the first j samples. A random permutation [math]\sigma_r[/math] is sampled from the [math]s+1[/math] independent random permutations of the training dataset. The random permutation, says [math]\sigma_r[/math], will then contribute to our construction of tree, [math]T_t[/math].

A gradient is computed at each step such that [math]grad_{r,j}(i)=\frac{\delta{L(y_i,M_{r,j}(i))}}{\delta{s}}[/math]. The leaf value for the tree constructed based on the i-th sample will then be equals to the average of the gradients computed, which can be written as: $$\text{avg } grad_{r, \sigma_r(i)-1}$$ When a tree, [math]T_t[/math] is constructed, the tree itself is used to boost all the existing models [math]M_{r',j}[/math]. Finally, in our final model, [math]F[/math], the leaf values are computed using the standard gradient boosting procedure. Recall that [math]\sigma_0[/math] is used to determine the final leaf values. Therefore, once we obtain our final model, we match the training samples, says [math]i^{th}[/math] sample, to [math]leaf_0(i)[/math] and so on. See Figure 2 for the detailed algorithm of how CatBoost build a decision tree.

Catboost tree algorithm.png
Figure 2: Algorithm to build a tree in Catboost



CatBoost Results

CatBoost is implemented as an algorithm for gradient boosting on decision trees. The algorithm is compared with the most popular open-source libraries – XGBoost and LightBGM. Categorical features are preprocessed using Ordered TS method for CatBoost. The results measured by logloss and zero-one loss are presented in Table 1. The statistical significance of performance is also presented in Table 1.

Image: 500 pixels
Table 1: Comparison with baselines: logloss / zero-one loss (relative increase for baselines).

Besides, the running time for CatBoost Plain and LightGBM are the fastest ones followed by Ordered mode, which is about 1.7 times slower.

Comparison between boosting modes of CatBoost: Plain and Ordered is performed on all considered datasets, and the results are presented in Table 2. It is evident that Ordered mode is especially effective on smaller datasets, which supports the hypothesis that a larger bias has a negative effect on performance.

Image: 600 pixels
Table 2: Plain boosting mode: logloss, zeroone loss and their change relative to Ordered boosting mode.

As illustrated in Figure 2, CatBoost is trained in Ordered and Plain modes on randomly filtered datasets to compare the generated losses. The relative performance of Plain modes becomes worse as the dataset size decreases.

Image: 500 pixels
Figure 2: Relative error of Plain boosting mode compared to Ordered boosting mode depending on the fraction of the dataset.

Different TSs options of CatBoost in Ordered boosting mode are being compared and the outcomes can be found in Table 3. Ordered TS used in CatBoost outscored all other approaches significantly. Among the baselines, the holdout TS is the best for a majority of the datasets.

Image: 500 pixels
Table 3: Comparison of target statistics, relative change in logloss / zero-one loss compared to ordered TS.

Conclusion

CatBoost has two unique advancements: the implementation of ordered boosting and ordered TS to tackle the problem of prediction shift caused by target leakage present in all existing implementations of gradient boosting. The empirical result shows that CatBoost overperforms other GBDT packages on most of the datasets and thus CatBoost is an effective tool for use in supervised machine learning technique.

Critiques

Strength

1) The proposed algorithm and current statistical issues are presented in a simple manner

2) Solid empirical study of the new algorithm compared to current methodologies such as XGBoost and lightGBM


Weakness

1) This paper performs the experiment on heterogenous, categorical datasets. It does not show the performance of CatBoost relative to XGBoost and LightBoost when working with homogenous data. Hence, it may be biased to state that CatBoost outperforms other leading GBDT packages.

2) The tasks in the experiment are classification tasks. Author should include regression task to determine if the result holds for regression problem.

3) The hyper-parameter setting such as iteration, maximum tree depth and so on can impact CatBoost's performance relative to other GBDT implementation. CatBoost's Oblivious Decision Tree (ODT) are balanced by definition. The "maximum tree depth" will have an impact on the amount of memory and running time. Iteration specifies the maximum number of decision tree CatBoost will construct. It is possible that the author tune their hyperpararameter so that it looks better than for the baselines.

References

[1] L. Bottou and Y. L. Cun. Large scale online learning. In Advances in neural information processing systems, pages 217–224, 2004.

[2] L. Breiman. Out-of-bag estimation, 1996.

[3] L. Breiman. Using iterated bagging to debias regressions. Machine Learning, 45(3):261–277, 2001.

[4] L. Breiman, J. Friedman, C. J. Stone, and R. A. Olshen. Classification and regression trees. CRC press, 1984.

[5] R. Caruana and A. Niculescu-Mizil. An empirical comparison of supervised learning algorithms. In Proceedings of the 23rd international conference on Machine learning, pages 161–168. ACM, 2006.

[6] B. Cestnik et al. Estimating probabilities: a crucial task in machine learning. In ECAI, volume 90, pages 147–149, 1990.

[7] O. Chapelle, E. Manavoglu, and R. Rosales. Simple and scalable response prediction for display advertising. ACM Transactions on Intelligent Systems and Technology (TIST), 5(4):61, 2015.

[8] T. Chen and C. Guestrin. Xgboost: A scalable tree boosting system. In Proceedings of the 22Nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 785–794. ACM, 2016.

[9] M. Ferov and M. Modr `y. Enhancing lambdamart using oblivious trees. arXiv preprint arXiv:1609.05610, 2016.

[10] J. Friedman, T. Hastie, and R. Tibshirani. Additive logistic regression: a statistical view of boosting. The annals of statistics, 28(2):337–407, 2000.

[11] J. Friedman, T. Hastie, and R. Tibshirani. The elements of statistical learning, volume 1. Springer series in statistics New York, 2001.

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