Learning Sparse High-Dimensional Matrix-Valued Graphical Models From Dependent Data
<|reference_start|>Learning Sparse High-Dimensional Matrix-Valued Graphical Models From Dependent Data: 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.<|reference_end|>
@article{tugnait2024learning,
    title={Learning Sparse High-Dimensional Matrix-Valued Graphical Models From
  Dependent Data},
    author={Jitendra K Tugnait},
    journal={arXiv preprint arXiv:2404.19073},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.19073},
    primaryClass={stat.ML cs.LG eess.SP}
}