An increasing number of projects in neuroscience require statistical analysis of high-dimensional data, as, for instance, in the prediction of behavior from neural firing or in the operation of artificial devices from brain recordings in brain-machine interfaces. Although prevalent, classical linear analysis techniques are often numerically fragile in high dimensions due to irrelevant, redundant, and noisy information. We developed a robust Bayesian linear regression algorithm that automatically detects relevant features and excludes irrelevant ones, all in a computationally efficient manner. In comparison with standard linear methods, the new Bayesian method regularizes against overfitting, is computationally efficient (unlike previously proposed variational linear regression methods, is suitable for data sets with large numbers of samples and a very high number of input dimensions) and is easy to use, thus demonstrating its potential as a drop-in replacement for other linear regression techniques. We evaluate our technique on synthetic data sets and on several neurophysiological data sets. For these neurophysiological data sets we address the question of whether EMG data collected from arm movements of monkeys can be faithfully reconstructed from neural activity in motor cortices. Results demonstrate the success of our newly developed method, in comparison with other approaches in the literature, and, from the neurophysiological point of view, confirms recent findings on the organization of the motor cortex. Finally, an incremental, real-time version of our algorithm demonstrates the suitability of our approach for real-time interfaces between brains and machines.

An increasing number of projects in neuroscience requires the sta- tistical analysis of high dimensional data sets, as, for instance, in predicting behavior from neural firing or in operating artificial de- vices from brain recordings in brain-machine interfaces. Linear analysis techniques remain prevalent in such cases, but classical linear regression approaches are often numerically too fragile in high dimensions. In this paper, we address the question of whether EMG data collected from arm movements of monkeys can be faith- fully reconstructed with linear approaches from neural activity in primary motor cortex (M1). To achieve robust data analysis, we develop a full Bayesian approach to linear regression that auto- matically detects and excludes irrelevant features in the data, reg- ularizing against overfitting. In comparison with ordinary least squares, stepwise regression, partial least squares, LASSO regres- sion and a brute force combinatorial search for the most predictive input features in the data, we demonstrate that the new Bayesian method offers a superior mixture of characteristics in terms of reg- ularization against overfitting, computational efficiency and ease of use, demonstrating its potential as a drop-in replacement for other linear regression techniques. As neuroscientific results, our anal- yses demonstrate that EMG data can be well predicted from M1 neurons, further opening the path for possible real-time interfaces between brains and machines.