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.

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.

Recent studies have utilized sparse classifications to predict categorical variables from high-dimensional brain activity signals to expose human's intentions and mental states, selecting the relevant features automatically in the model training process. However, existing sparse classification models will likely be prone to the performance degradation which is caused by noise inherent in the brain recordings. To address this issue, we aim to propose a new robust and sparse classification algorithm in this study. To this end, we introduce the correntropy learning framework into the automatic relevance determination based sparse classification model, proposing a new correntropy-based robust sparse logistic regression algorithm. To demonstrate the superior brain activity decoding performance of the proposed algorithm, we evaluate it on a synthetic dataset, an electroencephalogram (EEG) dataset, and a functional magnetic resonance imaging (fMRI) dataset. The extensive experimental results confirm that not only the proposed method can achieve higher classification accuracy in a noisy and high-dimensional classification task, but also it would select those more informative features for the decoding scenarios. Integrating the correntropy learning approach with the automatic relevance determination technique will significantly improve the robustness with respect to the noise, leading to more adequate robust sparse brain decoding algorithm. It provides a more powerful approach in the real-world brain activity decoding and the brain-computer interfaces.

The Partial Least Square Regression (PLSR) exhibits admirable competence for predicting continuous variables from inter-correlated brain recordings in the brain-computer interface. However, PLSR is in essence formulated based on the least square criterion, thus, being non-robust with respect to noises. The aim of this study is to propose a new robust implementation for PLSR. To this end, the maximum correntropy criterion (MCC) is used to propose a new robust variant of PLSR, called as Partial Maximum Correntropy Regression (PMCR). The half-quadratic optimization is utilized to calculate the robust projectors for the dimensionality reduction, and the regression coefficients are optimized by a fixed-point approach. We evaluate the proposed PMCR with a synthetic example and the public Neurotycho electrocorticography (ECoG) datasets. The extensive experimental results demonstrate that, the proposed PMCR can achieve better prediction performance than the conventional PLSR and existing variants with three different performance indicators in high-dimensional and noisy regression tasks. PMCR can suppress the performance degradation caused by the adverse noise, ameliorating the decoding robustness of the brain-computer interface.

The framework of information theoretic learning (ITL) has been verified as a powerful approach for robust machine learning, which improves robustness significantly in regression, feature extraction, dimensionality reduction and so on. Nevertheless, few studies utilize ITL for robust classification. In this study, we attempt to improve the robustness of the logistic regression, a fundamental method in classification, through analyzing the characteristic when the model is affected by outliers. We propose an ITL-based variant that learns by the error distribution, the performance of which is experimentally evaluated on two toy examples and several public datasets, compared with two traditional methods and two states of the art. The results demonstrate that the novel method can outperform the states of the art evidently in some cases, and behaves with desirable potential to achieve better robustness in complex situations than existing methods.