Globalized distributionally robust chance-constrained support vector machine based on core sets
Yueyao Li, Chenglong Bao, Wenxun Xing
TL;DR
This work tackles uncertainty in SVM by introducing a globalized distributionally robust chance-constrained SVM (GDRC SVM) that uses per-class moment-based ambiguity sets and core-set constraints to focus robustness on regions near the potential separating hyperplane. It derives a semidefinite programming (SDP) reformulation for exact solutions under appropriate core-set choices and distance functions, and proposes a PCA-based approximation to scale to high-dimensional data. The core-set constraints reduce conservatism and direct attention to influential data, improving classification accuracy, while the PCA approach provides substantial speedups with controlled approximation errors. Empirical results on simulated and real datasets show that GDRC SVM achieves higher robustness and accuracy than standard SVM and existing distributionally robust variants, with practical scalability achieved through the PCA-based approximation.
Abstract
Support vector machine (SVM) is a well known binary linear classification model in supervised learning. This paper proposes a globalized distributionally robust chance-constrained (GDRC) SVM model based on core sets to address uncertainties in the dataset and provide a robust classifier. The globalization means that we focus on the uncertainty in the sample population rather than the small perturbations around each sample point. The uncertainty is mainly specified by the confidence region of the first- and second-order moments. The core sets are constructed to capture some small regions near the potential classification hyperplane, which helps improve the classification quality via the expected distance constraint of the random vector to core sets. We obtain the equivalent semi-definite programming reformulation of the GDRC SVM model under some appropriate assumptions. To deal with the large-scale problem, an approximation approach based on principal component analysis is applied to the GDRC SVM. The numerical experiments are presented to illustrate the effectiveness and advantage of our model.