Generalized Connectivity Matrix Response Regression with Applications in Brain Connectivity Studies

TL;DR

This paper introduces a generalized matrix response regression model for analyzing multi-subject brain connectivity networks, capturing population patterns and covariate effects, with proven consistency and demonstrated effectiveness in simulations and real data.

Contribution

It proposes a novel low-rank plus sparse tensor regression model for multi-subject network data, along with an efficient estimation algorithm and theoretical guarantees.

Findings

Accurate recovery of population-level connectivity patterns.

Consistent graph community detection and edge selection.

Validated effectiveness through simulations and brain studies.

Abstract

Multiple-subject network data are fast emerging in recent years, where a separate connectivity matrix is measured over a common set of nodes for each individual subject, along with subject covariates information. In this article, we propose a new generalized matrix response regression model, where the observed networks are treated as matrix-valued responses and the subject covariates as predictors. The new model characterizes the population-level connectivity pattern through a low-rank intercept matrix, and the effect of subject covariates through a sparse slope tensor. We develop an efficient alternating gradient descent algorithm for parameter estimation, and establish the non-asymptotic error bound for the actual estimator from the algorithm, which quantifies the interplay between the computational and statistical errors. We further show the strong consistency for graph community recovery, as well as the edge selection consistency. We demonstrate the efficacy of our method through simulations and two brain connectivity studies.