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We develop a new modeling framework for Inter-Subject Analysis (ISA). Thegoal of ISA is to explore the dependency structure between different subjectswith the intra-subject dependency as nuisance. It has important applications inneuroscience to explore the functional connectivity between brain regions undernatural stimuli. Our framework is based on the Gaussian graphical models, underwhich ISA can be converted to the problem of estimation and inference of theinter-subject precision matrix. The main statistical challenge is that we donot impose sparsity constraint on the whole precision matrix and we only assumethe inter-subject part is sparse. For estimation, we propose to estimate analternative parameter to get around the non-sparse issue and it can achieveasymptotic consistency even if the intra-subject dependency is dense. Forinference, we propose an "untangle and chord" procedure to de-bias ourestimator. It is valid without the sparsity assumption on the inverse Hessianof the log-likelihood function. This inferential method is general and can beapplied to many other statistical problems, thus it is of independenttheoretical interest. Numerical experiments on both simulated and brain imagingdata validate our methods and theory.

Inter-Subject Analysis: Inferring Sparse Interactions with Dense Intra-Graphs