Adaptive sparseness for correntropy-based robust regression via automatic relevance determination
This work addresses hyper-parameter tuning for robust regression, which is an incremental improvement for machine learning practitioners dealing with noisy data.
The paper tackles the problem of tuning hyper-parameters in robust regression by integrating the maximum correntropy criterion with automatic relevance determination in a Bayesian framework, resulting in improved prediction performance and feature selection capability compared to existing methods.
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.