  Sparse Bayesian learning has promoted many effective frameworks for brain
activity decoding, especially for the reconstruction of muscle activity.
However, existing sparse Bayesian learning mainly employs 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 significant performance degradation for sparse Bayesian learning
method. The goal of this paper is to propose a new robust implementation for
sparse Bayesian learning, so that robustness and sparseness can be realized
simultaneously. Motivated by the great robustness of maximum correntropy
criterion (MCC), we proposed an integration of MCC into 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 used the automatic relevance determination (ARD) technique for
the sparse prior distribution. To fully evaluate the proposed method, a
synthetic dataset and a real-world muscle activity reconstruction task with two
different brain modalities were employed. Experimental results showed that our
proposed sparse Bayesian correntropy learning framework improves significantly
the robustness in a noisy regression task. The proposed method can realize
higher correlation coefficient and lower root mean squared error in the
real-world muscle activity reconstruction tasks. Sparse Bayesian correntropy
learning provides a powerful tool for neural decoding which can promote the
development of brain-computer interfaces.
