Multiple matrix Gaussian graphs estimation
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2018 · Volume 80 · Issue 5
Abstract
Matrix-valued data, where the sampling unit is a matrix consisting of rows and columns of measurements, are emerging in numerous scientific and business applications. Matrix Gaussian graphical models are a useful tool to characterize the conditional dependence structure of rows and columns. We employ non-convex penalization to tackle the estimation of multiple graphs from matrix-valued data under a matrix normal distribution. We propose a highly efficient non-convex optimization algorithm that can scale up for graphs with hundreds of nodes. We establish the asymptotic properties of the estimator, which requires less stringent conditions and has a sharper probability error bound than existing results. We demonstrate the efficacy of our proposed method through both simulations and real functional magnetic resonance imaging analyses.
Keywords
Conditional independence, Gaussian graphical model, Matrix normal distribution, Non-convex penalization, Resting state functional magnetic resonance imaging, Sparsistency
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