Maximum Correntropy Criterion Regression models with tending-to-zero scale parameters
This work addresses robustness in regression for statistical learning, but it is incremental as it extends existing MCCR models by focusing on a specific parameter regime.
The paper investigates Maximum Correntropy Criterion Regression (MCCR) models with scale parameters that tend to zero, revealing an optimal asymptotic learning rate of O(n^{-1}) as sample size increases, and compares their robustness against Huber and least square regression on finite samples and real data.
Maximum correntropy criterion regression (MCCR) models have been well studied within the frame of statistical learning when the scale parameters take fixed values or go to infinity. This paper studies the MCCR models with tending-to-zero scale parameters. It is revealed that the optimal learning rate of MCCR models is ${\mathcal{O}}(n^{-1})$ in the asymptotic sense when the sample size $n$ goes to infinity. In the case of finite samples, the performances on robustness of MCCR, Huber and the least square regression models are compared. The applications of these three methods on real data are also displayed.