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

• Published in: Applied mathematical modelling 2023-04, Vol.116, p.735-748
• Main Authors: Pidnebesna, Anna, Fajnerová, Iveta, Horáček, Jiří, Hlinka, Jaroslav
• Format: Article
• Language: English
• Subjects: BOLD; Deconvolution; FMRI; Mixtures with varying concentrations; Neuronal signal estimation
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2022.11.034

•Sparse linear regression methods have become ubiquitous in the mathematical modelling and engineering practice•We propose a novel approach that instead of selecting a single regularized solutions utilizes the whole family•The method is presented on a deconvolution problem, motivated by estimation of neuronal activity from indirect measurements•Numerical simulations show favorable performance in comparison with standard approaches in a range of realistic scenarios•This advantage is finally documented in selected functional magnetic resonance imaging datasets with known ground truth Sparse linear regression methods including the well-known LASSO and the Dantzig selector have become ubiquitous in the engineering practice, including in medical imaging. Among other tasks, they have been successfully applied for the estimation of neuronal activity from functional magnetic resonance data without prior knowledge of the stimulus or activation timing, utilizing an approximate knowledge of the hemodynamic response to local neuronal activity. These methods work by generating a parametric family of solutions with different sparsity, among which an ultimate choice is made using an information criteria. We propose a novel approach, that instead of selecting a single option from the family of regularized solutions, utilizes the whole family of such sparse regression solutions. Namely, their ensemble provides a first approximation of probability of activation at each time-point, 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 eventually deciding on the verity of activation at each time-point. We show in extensive numerical simulations that this 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 in selected fMRI task datasets.