A Distributionally-robust Approach for Finding Support Vector Machines

The classical SVM is an optimization problem minimizing the hinge losses of mis-classified samples with the regularization term. When the sample size is small or data has noise, it is possible that the classifier obtained with training data may not generalize well to pop- ulation, since the samples may not accurately represent the true population distribution. We propose a distributionally-robust framework for Support Vector Machines (DR-SVMs). We build an ambiguity set for the population distribution based on samples using the Kan- torovich metric. DR-SVMs search the classifier that minimizes the sum of regularization term and the hinge loss function for the worst-case population distribution among the ambi- guity set. We provide semi-infinite programming formulation of the DR-SVMs and propose a cutting-plane algorithm to solve the problem. Computational results on simulated data and real data from University of California, Irvine Machine Learning Repository show that the DR-SVMs outperform the SVMs in terms of the Area Under Curve (AUC) measures on several test problems.



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