A PAC bound for approximate support vector machines

Abstract

We study a class of algorithms that speed up the training process of support vector machines (SVMs) by returning an approximate SVM. We focus on algorithms that reduce the size of the optimization problem by extracting from the original training dataset a small number of representatives arid using these representatives to train an approximate SVM. The main contribution of this paper is a PAC-style generalization bound for the resulting approximate SVM, which provides a learning theoretic justification for using the approximate SVM in practice. The proved bound also generalizes and includes as a special case the generalization bound for the exact SVM, which denotes the SVM given by the original training dataset in this paper.