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.

翻译：针对许多机器学习场景中稀疏性和鲁棒性这两个重要特性，本研究以基于最大相关熵准则（MCC）的鲁棒回归算法为对象，探讨在贝叶斯框架下将MCC方法与自动相关性确定（ARD）技术相融合，从而使基于MCC的鲁棒回归能够实现自适应稀疏性。具体而言，我们利用MCC中隐含的噪声假设推导出显式似然函数，并通过变分贝叶斯推断实现带有ARD先验的最大后验（MAP）估计。与现有的鲁棒稀疏L1正则化MCC回归相比，所提出的MCC-ARD回归能够消除对控制正则化强度的超参数进行繁琐调参的需求。此外，如噪声高维仿真研究所证实的，MCC-ARD相比L1正则化MCC展现出更优的预测性能与特征选择能力。