Considering Span of Support Vector Bounds in the Context of Computational Learning Theory

This report describes a recent bound on expected support vector machine (SVM) generalization error [3] and frames this work in the context of computational learning theory [1], discussing the practical value of these bounds and the value to our mathematical understanding of machine learning. The fundamentals of computational learning theory are first outlined: PAC learning is defined, an example of PAC learning is given, and the Vapnik-Chervonenkis (VC) dimension is defined and related to PAC learning. Support vector machines are then briefly described. The span of support vector concept (and the bound on expected error that is based upon it) is described. The SVM bound using span of support vectors is given for the case of separable data and the proof given in [3] is outlined.