Mixture Components Inference for Sparse Regression: Introduction and Application for Estimation of Neuronal Signal from fMRI BOLD

Sparse linear regression methods including the well-known LASSO and Dantzig selector have become ubiquitous in engineering practice, medical imaging. Among other tasks, they been successfully applied for estimation of neuronal activity from functional magnetic resonance data without prior knowledge stimulus or activation timing, utilizing an approximate hemodynamic response to local activity. These work by generating a parametric family solutions with different sparsity, among which ultimate choice is made using information criteria. We propose novel approach, that instead selecting single option regularized solutions, utilizes whole such sparse solutions. Namely, their ensemble provides first approximation probability at each time-point, together conditional distributions estimated theory mixtures varying concentrations, serve as inputs Bayes classifier eventually deciding on verity time-point. show extensive numerical simulations this new method performs favourably comparison standard approaches range realistic scenarios. This mainly due avoidance overfitting underfitting commonly plague based combined model selection methods, corrected Akaike Information Criterion. advantage finally documented selected fMRI task datasets.