We consider the problem of inferring the conditional independence graph (CIG) of a sparse, highdimensional, stationary matrixvariate Gaussian time series. All past work on highdimensional matrix graphical models assumes that independent and identically distributed (i.i.d.) observations of the matrixvariate are available. Here we allow dependent observations. We consider a sparsegroup lassobased frequencydomain formulation of the problem with a Kroneckerdecomposable power spectral density (PSD), and solve it via an alternating direction method of multipliers (ADMM) approach. The problem is biconvex which is solved via flipflop 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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Sparse HighDimensional MatrixValued Graphical Model Learning from Dependent Data
We consider the problem of inferring the conditional independence graph (CIG) of a sparse, highdimensional, stationary matrixvariate Gaussian time series. All past work on matrix graphical models assume that i.i.d. observations of matrixvariate are available. Here we allow dependent observations. We consider a sparsegroup lasso based frequencydomain formulation of the problem with a Kroneckerdecomposable power spectral density (PSD), and solve it via an alternating direction method of multipliers (ADMM) approach. The problem is biconvex which is solved via flipflop optimization. We provide sufficient conditions for local convergence in the Frobenius norm of the inverse PSD estimators to the true value. This results also yields a rate of convergence. We illustrate our approach using numerical examples.
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 Award ID(s):
 2040536
 NSFPAR ID:
 10462219
 Date Published:
 Journal Name:
 2023 IEEE Statistical Signal Processing Workshop (SSP)
 Page Range / eLocation ID:
 344 to 348
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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We consider the problem of inferring the conditional independence graph (CIG) of a highdimensional stationary multivariate Gaussian time series. A sparsegroup lassobased frequencydomain formulation of the problem has been considered in the literature where the objective is to estimate the sparse inverse power spectral density (PSD) of the data via optimization of a sparsegroup lasso based penalized loglikelihood cost function that is formulated in the frequencydomain. The CIG is then inferred from the estimated inverse PSD. Optimization in the previous approach was performed using an alternating minimization (AM) approach whose performance depends upon choice of a penalty parameter. In this paper we investigate an alternating direction method of multipliers (ADMM) approach for optimization to mitigate dependence on the penalty parameter. We also investigate selection of the tuning parameters based on Bayesian information criterion, and illustrate our approach using synthetic and real data. Comparisons with the "usual" i.i.d. modeling of time series for graph estimation are also provided.more » « less