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

• URL: http://arxiv.org/abs/2404.19073v1
• Date: Mon, 29 Apr 2024 19:32:50 GMT
• Title: Learning Sparse High-Dimensional Matrix-Valued Graphical Models From Dependent Data
• Authors: Jitendra K Tugnait,
• Abstract summary: We consider the problem of inferring the conditional independence graph (CIG) of a sparse, high-dimensional, stationary matrix- Gaussian time series. We consider a sparse-based formulation of the problem with a Kronecker-decomposable power spectral density (PSD) We illustrate our approach using numerical examples utilizing both synthetic and real data.
• Score: 12.94486861344922
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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