Estimating Sparse Neuronal Signal from Hemodynamic Response: the Mixture Components Inference Approach

The approximate knowledge of the hemodynamic response to neuronal activity is widely used in statistical testing of effects of external stimulation, but has also been applied to estimate the neuronal activity directly from functional magnetic resonance data without knowing the stimulus timing. To this end, sparse linear regression methods have been previously used, including the well-known LASSO and the Dantzig selector. These methods generate a parametric family of solutions with different sparsity, among which a choice is finally based using some information criteria. As an alternative we propose a novel approach that instead utilizes the whole family of sparse regression solutions. Their ensemble provides a first approximation of probability of activation at each timepoint, and together with the conditional neuronal activity distributions estimated with the theory of mixtures with varying concentrations, they serve as the inputs to a Bayes classifier ultimately deciding between the true and false activations. As we show in extensive numerical simulations, the new method performs favourably in comparison with standard approaches in a range of realistic scenarios. This is mainly due to the avoidance of overfitting and underfitting that commonly plague the solutions based on sparse regression combined with model selection methods, including the corrected Akaike Information Criterion. This advantage is finally documented on fMRI task dataset.