Robust and Distributionally Robust Optimization Models for Linear Support Vector Machine
针对训练数据有噪声时两类点线性不可分的问题，提出了基于超矩形或超椭球不确定集的鲁棒模型和基于矩的分布鲁棒优化模型，实验表明鲁棒分类器在小样本数据上效果更好，分布鲁棒方法在高维数据上能提高预测准确率。
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.