Robustness of Maximum Correntropy Estimation Against Large Outliers

TL;DR

This paper analyzes the robustness of maximum correntropy estimation in linear models with large outliers, deriving bounds on estimation error and demonstrating its effectiveness in outlier scenarios.

Contribution

It provides theoretical insights and bounds on the estimation error of MCC under large outliers, showing its robustness in scalar linear errors-in-variables models.

Findings

MCC can produce estimates close to true parameters despite large outliers.

Derived an upper bound on the estimation error under certain conditions.

Illustrative examples confirm the theoretical results.

Abstract

The maximum correntropy criterion (MCC) has recently been successfully applied in robust regression, classification and adaptive filtering, where the correntropy is maximized instead of minimizing the well-known mean square error (MSE) to improve the robustness with respect to outliers (or impulsive noises). Considerable efforts have been devoted to develop various robust adaptive algorithms under MCC, but so far little insight has been gained as to how the optimal solution will be affected by outliers. In this work, we study this problem in the context of parameter estimation for a simple linear errors-in-variables (EIV) model where all variables are scalar. Under certain conditions, we derive an upper bound on the absolute value of the estimation error and show that the optimal solution under MCC can be very close to the true value of the unknown parameter even with outliers (whose values can be arbitrarily large) in both input and output variables. Illustrative examples are presented to verify and clarify the theory.