Maximum Correntropy Criterion Regression models with tending-to-zero scale parameters

TL;DR

This paper investigates maximum correntropy criterion regression models with scale parameters approaching zero, revealing optimal learning rates and comparing robustness with Huber and least squares methods on real data.

Contribution

It introduces the analysis of MCCR models with tending-to-zero scale parameters and compares their robustness with other regression methods.

Findings

Optimal learning rate is O(n^{-1}) for large samples.

MCCR shows robustness advantages over Huber and least squares.

Applications on real data demonstrate practical effectiveness.

Abstract

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.