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Robust and Distributionally Robust Optimization Models for Linear Support Vector Machine
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DOI：10.1016/j.cor.2022.105930.png)
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Abstract
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In this paper we present novel data-driven optimization models for Support Vector Machines (SVM), with the aim of linearly separating two sets of points that have non-disjoint convex closures. Traditional classification algorithms assume that the training data points are always known exactly. However, real-life data are often subject to noise. To handle such uncertainty, we formulate robust models with uncertainty sets in the form of hyperrectangles or hyperellipsoids, and propose a moment-based distributionally robust optimization model enforcing limits on first-order deviations along principal directions. All the formulations reduce to convex programs. The efficiency of the new classifiers is evaluated on real-world databases. Experiments show that robust classifiers are especially beneficial for data sets with a small number of observations. As the dimension of the data sets increases, features behavior is gradually learned and higher levels of out-of-sample accuracy can be achieved via the considered distributionally robust optimization method. The proposed formulations, overall, allow finding a trade-off between increasing the average performance accuracy and protecting against uncertainty, with respect to deterministic approaches.
Keywords:
Machine Learning
Support Vector Machine
Robust optimization
Distributionally robust optimization
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