Learning Sparse High-Dimensional Matrix-Valued Graphical Models From Dependent Data

TL;DR

This paper introduces a method for inferring the conditional independence graph of high-dimensional, matrix-variate Gaussian time series with dependent data, using a frequency-domain sparse-group lasso approach and ADMM optimization.

Contribution

It extends graphical model inference to dependent data scenarios with a novel frequency-domain formulation and provides convergence guarantees for the estimators.

Findings

Method successfully infers CIG in synthetic data

Approach applied to real data demonstrating practical utility

Provides convergence conditions and rate for the estimators

Abstract

We consider the problem of inferring the conditional independence graph (CIG) of a sparse, high-dimensional, stationary matrix-variate Gaussian time series. All past work on high-dimensional matrix graphical models assumes that independent and identically distributed (i.i.d.) observations of the matrix-variate are available. Here we allow dependent observations. We consider a sparse-group lasso-based frequency-domain formulation of the problem with a Kronecker-decomposable power spectral density (PSD), and solve it via an alternating direction method of multipliers (ADMM) approach. The problem is bi-convex which is solved via flip-flop optimization. We provide sufficient conditions for local convergence in the Frobenius norm of the inverse PSD estimators to the true value. This result also yields a rate of convergence. We illustrate our approach using numerical examples utilizing both synthetic and real data.