Consistency analysis of an empirical minimum error entropy algorithm

Jun Fan, Ting Hu, Qiang Wu, Ding Xuan Zhou

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)164-189
JournalApplied and Computational Harmonic Analysis
Volume41
Issue number1
DOIs
Publication statusPublished - 2016

Fingerprint

Dive into the research topics of 'Consistency analysis of an empirical minimum error entropy algorithm'. Together they form a unique fingerprint.

Cite this