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

arXiv: https://arxiv.org/abs/2404.19073 · HTML: https://mlsanity.com/paper/2404.19073/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 56 references that are in the map.
- First posted on arXiv 29 Apr 2024.

## Builds on (most cited first, 14 of 14)

- [Regularized estimation in sparse high-dimensional time series models](https://mlsanity.com/paper/1311.4175/) (2013)
- [Autoregressive Models for Matrix-Valued Time Series](https://mlsanity.com/paper/1812.08916/) (2018)
- [Tensor Graphical Lasso (TeraLasso)](https://mlsanity.com/paper/1705.03983/) (2017)
- [Graphical LASSO Based Model Selection for Time Series](https://mlsanity.com/paper/1410.1184/) (2014)
- [On Sparse High-Dimensional Graphical Model Learning For Dependent Time Series](https://mlsanity.com/paper/2111.07897/) (2021)
- [AR Identification of Latent-variable Graphical Models](https://mlsanity.com/paper/1405.0027/) (2014)
- [Identification of Sparse Reciprocal Graphical Models](https://mlsanity.com/paper/1806.04423/) (2018)
- [Sparse-Group Log-Sum Penalized Graphical Model Learning For Time Series](https://mlsanity.com/paper/2204.13824/) (2022)
- [Graph Estimation for Matrix-variate Gaussian Data](https://mlsanity.com/paper/1509.05453/) (2015)
- [Data-driven Link Prediction over Graphical Models](https://mlsanity.com/paper/2004.14187/) (2020)
- [Autoregressive Identification of Kronecker Graphical Models](https://mlsanity.com/paper/2004.14199/) (2020)
- [Nonparametric Identification of Kronecker Networks](https://mlsanity.com/paper/2206.05156/) (2022)
- [QUARKS: Identification of large-scale Kronecker Vector-AutoRegressive models](https://mlsanity.com/paper/1609.07518/) (2016)
- [Online Graph Topology Learning from Matrix-valued Time Series](https://mlsanity.com/paper/2107.08020/) (2021)

## Built on by (most cited first, 2 of 2)

- [High-Dimensional Sparse Data Low-rank Representation via Accelerated Asynchronous Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/2408.16592/) (2024)
- [Identification of Non-causal Graphical Models](https://mlsanity.com/paper/2410.09480/) (2024)

## Abstract (arXiv)

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.