Exploring an EM-algorithm for banded regression in computational neuroscience

Regression is a principal tool for relating brain responses to stimuli or tasks in computational neuroscience. This often involves fitting linear models with predictors that can be divided into groups, such as distinct stimulus feature subsets in encoding models or features of different neural response channels in decoding models. When fitting such models, it can be relevant to allow differential shrinkage of the different groups of regression weights. Here, we explore a framework that allows for straightforward definition and estimation of such models. We present an expectation-maximization algorithm for tuning hyperparameters that control shrinkage of groups of weights. We highlight properties, limitations, and potential use-cases of the model using simulated data. Next, we explore the model in the context of a BOLD fMRI encoding analysis and an EEG decoding analysis. Finally, we discuss cases where the model can be useful and scenarios where regularization procedures complicate model interpretation.