Robust and Distributionally Robust Optimization Models for Support Vector Machine with Application to Breast Cancer and Heart Disease Recognition
Abstract: In this paper we present novel data-driven optimization models for Support Vector Machine (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 distributionally robust optimization models 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 in medicine, requiring cancer detection and heart disease recognition. Experiments show that box robust classifiers might be overly-conservative, whereas higher levels of accuracy can be achieved when moments of the distributions are assumed exploiting the available information via distributionally robust optimization methods.
Keywords: Machine Learning; Support Vector Machine; Robust Optimization; Distributionally Robust Optimization; OR in Medicine.
Category 1: Applications -- OR and Management Sciences
Category 2: Robust Optimization
Citation: The manuscript has been submitted to an international journal on October 2, 2020.
Entry Submitted: 01/22/2021
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