Robustness of Maximum Correntropy Estimation Against Large Outliers
This work provides theoretical insight into the robustness of MCC against outliers, which is incremental as it builds on existing applications of MCC in robust regression and filtering.
The paper investigates how the maximum correntropy criterion (MCC) performs in parameter estimation for a linear errors-in-variables model with large outliers, deriving an upper bound on estimation error and showing that the optimal solution can remain close to the true parameter value even with arbitrarily large outliers in both input and output variables.
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.