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Stochastic Gradient Boosting (SGB) is a widely used approach toregularization of boosting models based on decision trees. It was shown that,in many cases, random sampling at each iteration can lead to bettergeneralization performance of the model and can also decrease the learningtime. Different sampling approaches were proposed, where probabilities are notuniform, and it is not currently clear which approach is the most effective. Inthis paper, we formulate the problem of randomization in SGB in terms ofoptimization of sampling probabilities to maximize the estimation accuracy ofsplit scoring used to train decision trees. This optimization problem has aclosed-form nearly optimal solution, and it leads to a new sampling technique,which we call Minimal Variance Sampling (MVS). The method both decreases thenumber of examples needed for each iteration of boosting and increases thequality of the model significantly as compared to the state-of-the art samplingmethods. The superiority of the algorithm was confirmed by introducing MVS as anew default option for subsampling in CatBoost, a gradient boosting libraryachieving state-of-the-art quality on various machine learning tasks.

Minimal Variance Sampling in Stochastic Gradient Boosting