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1. Graph Learning From Multivariate Dependent Time Series Via A Multi-Attribute Formulation

   https://doi.org/10.1109/ICASSP43922.2022.9746603  

   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. In a time series graph, each component of the vector series is represented by distinct node, and associations between components are represented by edges between the corresponding nodes. We formulate the problem as one of multi-attribute graph estimation for random vectors where a vector is associated with each node of the graph. At each node, the associated random vector consists of a time series component and its delayed copies. We present an alternating direction method of multipliers (ADMM) solution to minimize a sparse-group lasso penalized negative pseudo log-likelihood objective function to estimate the precision matrix of the random vector associated with the entire multi-attribute graph. The time series CIG is then inferred from the estimated precision matrix. A theoretical analysis is provided. Numerical results illustrate the proposed approach which outperforms existing frequency-domain approaches in correctly detecting the graph edges. 

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2. 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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3. Estimation of High-Dimensional Differential Graphs from Multi-Attribute Data

   https://doi.org/10.1109/ICASSP49357.2023.10095585  

   Tugnait, Jitendra K. ( June 2023 , ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP))

   We consider the problem of estimating differences in two Gaussian graphical models (GGMs) which are known to have similar structure. The GGM structure is encoded in its precision (inverse covariance) matrix. In many applications one is interested in estimating the difference in two precision matrices to characterize underlying changes in conditional dependencies of two sets of data. Existing methods for differential 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 analyze a group lasso penalized D-trace loss function approach for differential graph learning from multi-attribute data. An alternating direction method of multipliers (ADMM) algorithm is presented to optimize the objective function. Theoretical analysis establishing consistency in support recovery and estimation in high-dimensional settings is provided. We illustrate our approach using a numerical example where the multi-attribute approach is shown to outperform a single-attribute approach. 

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4. Learning High-Dimensional Differential Graphs From Multi-Attribute Data

   https://doi.org/10.1109/TSP.2023.3343553  

   Tugnait, Jitendra K. ( December 2023 , IEEE Transactions on Signal Processing)

   We consider the problem of estimating differences in two Gaussian graphical models (GGMs) which are known to have similar structure. The GGM structure is encoded in its precision (inverse covariance) matrix. In many applications one is interested in estimating the difference in two precision matrices to characterize underlying changes in conditional dependencies of two sets of data. Existing methods for differential graph estimation are based on single-attribute (SA) models where one associates a scalar random variable with each node. In multi-attribute (MA) graphical models, each node represents a random vector. In this paper, we analyze a group lasso penalized D-trace loss function approach for differential graph learning from multi-attribute data. An alternating direction method of multipliers (ADMM) algorithm is presented to optimize the objective function. Theoretical analysis establishing consistency in support recovery and estimation in high-dimensional settings is provided. Numerical results based on synthetic as well as real data are presented. 

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5. Delay Embedding for Matrix Graphical Model Learning from Dependent Data

   https://doi.org/10.1109/ICASSP48485.2024.10447097  

   Tugnait, Jitendra K ( April 2024 , IEEE)

   We consider the problem of inferring the conditional independence graph (CIG) of a sparse, high-dimensional, stationary matrix-variate Gaussian time series. The correlation function of the matrix series is Kronecker-decomposable. Unlike most past work on matrix graphical models, where independent and identically distributed (i.i.d.) observations of matrix-variate are assumed to be available, we allow time-dependent observations. We follow a time-delay embedding approach where with each matrix node, we associate a random vector consisting of a scalar series component and its time-delayed copies. A group-lasso penalized negative pseudo log-likelihood (NPLL) objective function is formulated to estimate a Kronecker-decomposable covariance matrix which allows for inference of the underlying CIG. The NPLL function is bi-convex and the Kronecker-decomposable covariance matrix is estimated via flip-flop optimization of the NPLL function. Each iteration of flip-flop optimization is solved via an alternating direction method of multipliers (ADMM) approach. Numerical results illustrate the proposed approach which outperforms an existing i.i.d. modeling based approach as well as an existing frequency-domain approach for dependent data, in correctly detecting the graph edges. 

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