mlsanityData to 14 Oct 2026

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

arXiv 2404.19073 ↗First posted 29 Apr 2024stat.ML cs.LG eess.SPcited by 2

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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.

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

14 of 56 references.

References · 14

  1. 2013Regularized estimation in sparse high-dimensional time series modelscited by 41
  2. 2018Autoregressive Models for Matrix-Valued Time Seriescited by 18
  3. 2017Tensor Graphical Lasso (TeraLasso)cited by 16
  4. 2014Graphical LASSO Based Model Selection for Time Seriescited by 13
  5. 2021On Sparse High-Dimensional Graphical Model Learning For Dependent Time Seriescited by 6
  6. 2014AR Identification of Latent-variable Graphical Modelscited by 5
  7. 2018Identification of Sparse Reciprocal Graphical Modelscited by 5
  8. 2022Sparse-Group Log-Sum Penalized Graphical Model Learning For Time Seriescited by 5
  9. 2015Graph Estimation for Matrix-variate Gaussian Datacited by 3
  10. 2020Data-driven Link Prediction over Graphical Modelscited by 2
  11. 2020Autoregressive Identification of Kronecker Graphical Modelscited by 2
  12. 2022Nonparametric Identification of Kronecker Networkscited by 2
2 more
  1. 2016QUARKS: Identification of large-scale Kronecker Vector-AutoRegressive modelscited by 1
  2. 2021Online Graph Topology Learning from Matrix-valued Time Seriescited by 1

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Cited by year

Citing papers per year: 2024: 2.

2 papers.

  1. 2024High-Dimensional Sparse Data Low-rank Representation via Accelerated Asynchronous Parallel Stochastic Gradient Descentcited by 0
  2. 2024Identification of Non-causal Graphical Modelscited by 0