Maximum Correntropy Estimation Is a Smoothed MAP Estimation

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Badong Chen, José Carlos Príncipe

Published: 2012, Last Modified: 21 Jan 2026IEEE Signal Process. Lett. 2012EveryoneRevisionsBibTeXCC BY-SA 4.0
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.