Learning Sparse High-Dimensional Matrix-Valued Graphical Models From Dependent Data
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910428446064640 |
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| author | Tugnait, Jitendra K |
| author_facet | Tugnait, Jitendra K |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_19073 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning Sparse High-Dimensional Matrix-Valued Graphical Models From Dependent Data Tugnait, Jitendra K Machine Learning Signal Processing 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. |
| title | Learning Sparse High-Dimensional Matrix-Valued Graphical Models From Dependent Data |
| topic | Machine Learning Signal Processing |
| url | https://arxiv.org/abs/2404.19073 |