Performance analysis for L\_2 kernel classification

Abstract

We provide statistical performance guarantees for a recently introduced kernel classifier that optimizes the L_2 or integrated squared error (ISE) of a difference of densities. The classifier is similar to a support vector machine (SVM) in that it is the solution of a quadratic program and yields a sparse classifier. Unlike SVMs, however, the L_2 kernel classifier does not involve a regularization parameter. We prove a distribution free concentration inequality for a cross-validation based estimate of the ISE, and apply this result to deduce an oracle inequality and consistency of the classifier on the sense of both ISE and probability of error. Our results can also be specialized to give performance guarantees for an existing method of L_2 kernel density estimation.

Tasks

Reproductions