Kernel-based maximum correntropy criterion with gradient descent method

Ting Hu

doi:10.3934/cpaa.2020186

Article Contents

2020, Volume 19, Issue 8: 4159-4177. Doi: 10.3934/cpaa.2020186

This issue Previous Article Computing eigenpairs of two-parameter Sturm-Liouville systems using the bivariate sinc-Gauss formula Next Article A numerical method to compute Fisher information for a special case of heterogeneous negative binomial regression

Kernel-based maximum correntropy criterion with gradient descent method

Ting Hu

School of Mathematics and Statistics, Wuhan University, Wuhan, China

Received: September 2019

Revised: December 2019

Published: May 2020

The author is supported by NSFC grant 11671307 and 11571078

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Abstract

In this paper, we study the convergence of the gradient descent method for the maximum correntropy criterion (MCC) associated with reproducing kernel Hilbert spaces (RKHSs). MCC is widely used in many real-world applications because of its robustness and ability to deal with non-Gaussian impulse noises. In the regression context, we show that the gradient descent iterates of MCC can approximate the target function and derive the capacity-dependent convergence rate by taking a suitable iteration number. Our result can nearly match the optimal convergence rate stated in the previous work, and in which we can see that the scaling parameter is crucial to MCC's approximation ability and robustness property. The novelty of our work lies in a sharp estimate for the norms of the gradient descent iterates and the projection operation on the last iterate.

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Mathematics Subject Classification: Primary: 68Q32, 62J02; Secondary: 41A46.

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