Sparse Bayesian correntropy learning for robust muscle activity reconstruction from noisy brain recordings

Sparse Bayesian learning has promoted many effective frameworks of brain activity decoding for the brain-computer interface, including the direct reconstruction of muscle activity using brain recordings. However, existing sparse Bayesian learning algorithms mainly use Gaussian distribution as error assumption in the reconstruction task, which is not necessarily the truth in the real-world application. On the other hand, brain recording is known to be highly noisy and contains many non-Gaussian noises, which could lead to large performance degradation for sparse Bayesian learning algorithms. The goal of this paper is to propose a novel robust implementation of sparse Bayesian learning so that robustness and sparseness can be realized simultaneously. Motivated by the exceptional robustness of maximum correntropy criterion (MCC), we proposed integrating MCC to the sparse Bayesian learning regime. To be specific, we derived the explicit error assumption inherent in the MCC, and then leveraged it for the likelihood function. Meanwhile, we utilized the automatic relevance determination technique as the sparse prior distribution. To fully evaluate the proposed method, a synthetic example and a real-world muscle activity reconstruction task with two different brain modalities were leveraged. Experimental results showed, our proposed sparse Bayesian correntropy learning framework significantly improves the robustness for the noisy regression tasks. Our proposed algorithm could realize higher correlation coefficients and lower root mean squared errors for the real-world muscle activity reconstruction scenario. Sparse Bayesian correntropy learning provides a powerful approach for brain activity decoding which will promote the development of brain-computer interface technology.