Online minimum error entropy algorithm with unbounded sampling

Abstract

Minimum error entropy (MEE) criterion is an important optimization method in information theoretic learning (ITL) and has been widely used and studied in various practical scenarios. In this paper, we shall introduce the online MEE algorithm for dealing with big datasets, associated with reproducing kernel Hilbert spaces (RKHS) and unbounded sampling processes. Explicit convergence rate will be given under the conditions of regularity of the regression function and polynomially decaying step sizes. Besides its low complexity, we will also show that the learning ability of online MEE is superior to the previous work in the literature. Our main techniques depend on integral operators on RKHS and probability inequalities for random variables with values in a Hilbert space.