Two Sample Inference for Populations of Graphical Models with Applications to Functional Connectivity

Abstract

Gaussian Graphical Models (GGM) are popularly used in neuroimaging studies based on fMRI, EEG or MEG to estimate functional connectivity, or relationships between remote brain regions. In multi-subject studies, scientists seek to identify the functional brain connections that are different between two groups of subjects, i.e. connections present in a diseased group but absent in controls or vice versa. This amounts to conducting two-sample large scale inference over network edges post graphical model selection, a novel problem we call Population Post Selection Inference. Current approaches to this problem include estimating a network for each subject, and then assuming the subject networks are fixed, conducting two-sample inference for each edge. These approaches, however, fail to account for the variability associated with estimating each subject's graph, thus resulting in high numbers of false positives and low statistical power. By using resampling and random penalization to estimate the post selection variability together with proper random effects test statistics, we develop a new procedure we call $R^3$ that solves these problems. Through simulation studies we show that $R^3$ offers major improvements over current approaches in terms of error control and statistical power. We apply our method to identify functional connections present or absent in autistic subjects using the ABIDE multi-subject fMRI study.

References in corpus (8)

• Confidence Intervals and Hypothesis Testing for High-Dimensional Regression
• Valid post-selection inference
• Sparse Inverse Covariance Matrix Estimation Using Quadratic Approximation
• Learning and comparing functional connectomes across subjects
• Asymptotic normality and optimalities in estimation of large Gaussian graphical models
• Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models
• Estimating Undirected Graphs Under Weak Assumptions
• Inference of Network Summary Statistics Through Network Denoising

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• Scalable Inference of Sparsely-changing Markov Random Fields with Strong Statistical Guarantees
• Paired Test of Matrix Graphs and Brain Connectivity Analysis
• Bayesian Edge Regression in Undirected Graphical Models to Characterize Interpatient Heterogeneity in Cancer