Fast rates of minimum error entropy with heavy-tailed noise

Abstract

In this paper, we investigate the performance of minimum error entropy (MEE) from a theoretical viewpoint. Owing to resistance of heavy-tailed noise or outliers, as an alternative to traditional robust empirical risk minimization schemes, MEE has drawn particular attention over the last decades and has been successfully used in machine learning. The purpose of this paper is to conduct refined learning theory analysis of MEE and establish its improved rates of convergence without the light-tailed noise. It shows that a new comparison theorem not only characterizes the regression calibration properties of MEE, but also refines the variance of analysis of learning theory.