Inter-Subject Analysis: Inferring Sparse Interactions with Dense Intra-Graphs
This work addresses a statistical challenge in neuroscience for analyzing functional connectivity between brain regions under natural stimuli, with incremental contributions to estimation and inference methods.
The paper tackles the problem of inferring sparse interactions between subjects in Inter-Subject Analysis (ISA) while allowing dense intra-subject dependencies, proposing a new modeling framework based on Gaussian graphical models with estimation and inference methods that achieve asymptotic consistency and validity without sparsity assumptions on the inverse Hessian.
We develop a new modeling framework for Inter-Subject Analysis (ISA). The goal of ISA is to explore the dependency structure between different subjects with the intra-subject dependency as nuisance. It has important applications in neuroscience to explore the functional connectivity between brain regions under natural stimuli. Our framework is based on the Gaussian graphical models, under which ISA can be converted to the problem of estimation and inference of the inter-subject precision matrix. The main statistical challenge is that we do not impose sparsity constraint 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 non-sparse 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.