Inter-Subject Analysis: A Partial Gaussian Graphical Model Approach

• Published in: Journal of the American Statistical Association Vol. 116; no. 534; pp. 746 - 755
• Main Authors: Ma, Cong, Lu, Junwei, Liu, Han
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis 03.04.2021; Taylor & Francis Ltd
• Subjects: Bias; Brain; Dependency; fMRI data; Functional connectivity; Gaussian graphical models; Graphical models; Neuroimaging; neurophysiology; normal distribution; Nuisance parameter; Parameter estimation; Regression analysis; Sample splitting; Sparsity; Statistical inference; Statistical methods; Statistics; Uncertainty assessment; Gaussian graphical models; Sample splitting; Uncertainty assessment; Nuisance parameter; fMRI data
• ISSN: 0162-1459; 1537-274X; 1537-274X
• DOI: 10.1080/01621459.2020.1841645

Different from traditional intra-subject analysis, the goal of inter-subject analysis (ISA) is to explore the dependency structure between different subjects with the intra-subject dependency as nuisance. ISA has important applications in neuroscience to study the functional connectivity between brain regions under natural stimuli. We propose a modeling framework for ISA that is based on Gaussian graphical models, under which ISA can be converted to the problem of estimation and inference of a partial Gaussian graphical model. The main statistical challenge is that we do not impose sparsity constraints on the whole precision matrix and we only assume the inter-subject part is sparse. For estimation, we propose to estimate an alternative parameter to get around the nonsparse issue and it can achieve asymptotic consistency even if the intra-subject dependency is dense. For inference, we propose an "untangle and chord" procedure to de-bias our estimator. It is valid without the sparsity assumption on the inverse Hessian of the log-likelihood function. This inferential method is general and can be applied to many other statistical problems, thus it is of independent theoretical interest. Numerical experiments on both simulated and brain imaging data validate our methods and theory. Supplementary materials for this article are available online.