Robust support vector machines via conic optimization

• URL: http://arxiv.org/abs/2402.01797v1
• Date: Fri, 2 Feb 2024 05:42:50 GMT
• Title: Robust support vector machines via conic optimization
• Authors: Valentina Cepeda, Andr\'es G\'omez, Shaoning Han
• Abstract summary: We consider the problem of convex computational machines robust to uncertainty. We show that the proposed estimator is competitive with the SVMs with the loss in outlier-free and better in the presence of outliers.
• Score: 0.8594140167290099
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We consider the problem of learning support vector machines robust to uncertainty. It has been established in the literature that typical loss functions, including the hinge loss, are sensible to data perturbations and outliers, thus performing poorly in the setting considered. In contrast, using the 0-1 loss or a suitable non-convex approximation results in robust estimators, at the expense of large computational costs. In this paper we use mixed-integer optimization techniques to derive a new loss function that better approximates the 0-1 loss compared with existing alternatives, while preserving the convexity of the learning problem. In our computational results, we show that the proposed estimator is competitive with the standard SVMs with the hinge loss in outlier-free regimes and better in the presence of outliers.

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