Title :
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
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;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2012.2204435
