Adaptive sparseness for correntropy-based robust regression via automatic relevance determination

TL;DR

This paper introduces an adaptive sparse regression method combining maximum correntropy criterion with automatic relevance determination, enabling robust, hyperparameter-free feature selection in noisy, high-dimensional data.

Contribution

It integrates MCC with ARD in a Bayesian framework for adaptive sparsity, eliminating the need for hyperparameter tuning in robust regression.

Findings

Outperforms L1-regularized MCC in prediction accuracy

Achieves superior feature selection in noisy, high-dimensional data

Removes hyperparameter tuning complexity

Abstract

Sparseness and robustness are two important properties for many machine learning scenarios. In the present study, regarding the maximum correntropy criterion (MCC) based robust regression algorithm, we investigate to integrate the MCC method with the automatic relevance determination (ARD) technique in a Bayesian framework, so that MCC-based robust regression could be implemented with adaptive sparseness. To be specific, we use an inherent noise assumption from the MCC to derive an explicit likelihood function, and realize the maximum a posteriori (MAP) estimation with the ARD prior by variational Bayesian inference. Compared to the existing robust and sparse L1-regularized MCC regression, the proposed MCC-ARD regression can eradicate the troublesome tuning for the regularization hyper-parameter which controls the regularization strength. Further, MCC-ARD achieves superior prediction performance and feature selection capability than L1-regularized MCC, as demonstrated by a noisy and high-dimensional simulation study.