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

arXiv: https://arxiv.org/abs/2302.00082 · HTML: https://mlsanity.com/paper/2302.00082/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 30 references that are in the map.
- First posted on arXiv 31 Jan 2023.

## Builds on (most cited first, 4 of 4)

- [Variational Relevance Vector Machines](https://mlsanity.com/paper/1301.3838/) (2013)
- [Generalized Correntropy for Robust Adaptive Filtering](https://mlsanity.com/paper/1504.02931/) (2015)
- [Correntropy-Based Logistic Regression with Automatic Relevance Determination for Robust Sparse Brain Activity Decoding](https://mlsanity.com/paper/2207.09693/) (2022)
- [Bias-Compensated Normalized Maximum Correntropy Criterion Algorithm for System Identification with Noisy Input](https://mlsanity.com/paper/1711.08677/) (2017)

## Built on by (most cited first, 3 of 3)

- [Sparse Bayesian Correntropy Learning for Robust Muscle Activity Reconstruction from Noisy Brain Recordings](https://mlsanity.com/paper/2404.15309/) (2024)
- [Correntropy-Based Improper Likelihood Model for Robust Electrophysiological Source Imaging](https://mlsanity.com/paper/2408.14843/) (2024)
- [Robust Sparse Bayesian Learning Based on Minimum Error Entropy for Noisy High-Dimensional Brain Activity Decoding](https://mlsanity.com/paper/2508.11657/) (2025)

## Abstract (arXiv)

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.