  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.
