Maximum Correntropy Estimation Is a Smoothed MAP Estimation

Author

Chen, Badong ; Príncipe, José C.

Author_Institution

Electr. & Comput. Eng. (ECE) Dept., Univ. of Florida, Gainesville, FL, USA

Volume

19

Issue

8

fYear

2012

Firstpage

491

Lastpage

494

Abstract

As a new measure of similarity, the correntropy can be used as an objective function for many applications. In this letter, we study Bayesian estimation under maximum correntropy (MC) criterion. We show that the MC estimation is, in essence, a smoothed maximum a posteriori (MAP) estimation, including the MAP and the minimum mean square error (MMSE) estimation as the extreme cases. We also prove that under a certain condition, when the kernel size in correntropy is larger than some value, the MC estimation will have a unique optimal solution lying in a strictly concave region of the smoothed posterior distribution.

Keywords

Bayes methods; entropy; least mean squares methods; maximum likelihood estimation; signal processing; Bayesian estimation; MAP estimation; MC criterion; MMSE estimation; concave region; kernel size; maximum a posteriori estimation; maximum correntropy estimation criterion; minimum mean square error; objective function; smoothed MAP estimation; smoothed posterior distribution; Convolution; Estimation; Kernel; Mean square error methods; Probability density function; Random variables; Smoothing methods; Correntropy; estimation; maximum a posteriori estimation; maximum correntropy estimation;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/LSP.2012.2204435

Filename

6216402