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1. Sparse-Group Log-Sum Penalized Graphical Model Learning For Time Series

   https://doi.org/10.1109/ICASSP43922.2022.9747446  

   Tugnait, Jitendra K. ( May 2022 , ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) |)

   We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. A sparse-group lasso based frequency-domain 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. The CIG is then inferred from the estimated inverse PSD. In this paper we investigate use of a sparse-group log-sum penalty (LSP) instead of sparse-group lasso penalty. An alternating direction method of multipliers (ADMM) approach for iterative optimization of the non-convex problem is presented. 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 utilizing both synthetic and real data. 

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2. New Results on Graphical Modeling of High-Dimensional Dependent Time Series

   https://doi.org/10.1109/IEEECONF53345.2021.9723239  

   Tugnait, Jitendra K. ( October 2021 , 2021 55th Asilomar Conference on Signals, Systems, and Computers)

   We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. A sparse-group lasso-based frequency-domain 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 sparse-group lasso based penalized log-likelihood cost function that is formulated in the frequency-domain. 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. 

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3. Sparse High-Dimensional Matrix-Valued Graphical Model Learning from Dependent Data

   https://doi.org/10.1109/SSP53291.2023.10208070  

   Tugnait, Jitendra K. ( July 2023 , 2023 IEEE Statistical Signal Processing Workshop (SSP))

   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 matrix graphical models assume that i.i.d. observations of 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 results also yields a rate of convergence. We illustrate our approach using numerical examples. 

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

   https://doi.org/10.1109/TSP.2024.3395897  

   Tugnait, Jitendra K ( May 2024 , IEEE Transactions on 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 biconvex 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. 

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5. Sparse-Group Non-convex Penalized Multi-Attribute Graphical Model Selection

   https://doi.org/10.23919/EUSIPCO54536.2021.9616255  

   Tugnait, Jitendra K. ( August 2021 , 2021 29th European Signal Processing Conference (EUSIPCO))

   We consider the problem of inferring the conditional independence graph (CIG) of high-dimensional Gaussian vectors from multi-attribute data. Most existing methods for graph estimation are based on single-attribute models where one associates a scalar random variable with each node. In multi-attribute graphical models, each node represents a random vector. In this paper we consider a sparse-group smoothly clipped absolute deviation (SG-SCAD) penalty instead of sparse-group lasso (SGL) penalty to regularize the problem. We analyze an SG-SCAD-penalized log-likelihood based objective function to establish consistency of a local estimator of inverse covariance. A numerical example is presented to illustrate the advantage of SG-SCAD-penalty over the usual SGL-penalty. 

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