Consistency analysis of an empirical minimum error entropy algorithm

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

40 Scopus Citations
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Detail(s)

Original languageEnglish
Pages (from-to)164-189
Journal / PublicationApplied and Computational Harmonic Analysis
Volume41
Issue number1
Online published23 Dec 2014
Publication statusPublished - Jul 2016

Abstract

In this paper we study the consistency of an empirical minimum error entropy (MEE) algorithm in a regression setting. We introduce two types of consistency. The error entropy consistency, which requires the error entropy of the learned function to approximate the minimum error entropy, is shown to be always true if the bandwidth parameter tends to 0 at an appropriate rate. The regression consistency, which requires the learned function to approximate the regression function, however, is a complicated issue. We prove that the error entropy consistency implies the regression consistency for homoskedastic models where the noise is independent of the input variable. But for heteroskedastic models, a counterexample is used to show that the two types of consistency do not coincide. A surprising result is that the regression consistency is always true, provided that the bandwidth parameter tends to infinity at an appropriate rate. Regression consistency of two classes of special models is shown to hold with fixed bandwidth parameter, which further illustrates the complexity of regression consistency of MEE. Fourier transform plays crucial roles in our analysis.

Research Area(s)

  • Error entropy consistency, Learning theory, Minimum error entropy, Regression consistency, Rényi's entropy