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1. Estimation of Multi-Attribute Differential Graphs with Non-Convex Penalties

   https://doi.org/10.1109/ICASSP49660.2025.10887671  

   Tugnait, Jitendra K (April 2025, IEEE)

   We consider the problem of estimating differences in two multi-attribute Gaussian graphical models (GGMs) which are known to have similar structure, using a penalized D-trace loss function with nonconvex penalties. The GGM structure is encoded in its precision (inverse covariance) matrix. Existing methods for multi-attribute differential graph estimation are based on a group lasso penalized loss function. In this paper, we consider a penalized D-trace loss function with nonconvex (log-sum and smoothly clipped absolute deviation (SCAD)) penalties. Two proximal gradient descent methods are presented to optimize the objective function. Theoretical analysis establishing local consistency in support recovery, local convexity and estimation in high-dimensional settings is provided. We illustrate our approach with a numerical example. 

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2. Learning Multi-Attribute Differential Graphs With Non-Convex Penalties

   https://doi.org/10.1109/ACCESS.2025.3559883  

   Tugnait, Jitendra K (January 2025, IEEE Access)

   We consider the problem of estimating differences in two multi-attribute Gaussian graphical models (GGMs) which are known to have similar structure, using a penalized D-trace loss function with non-convex penalties. The GGM structure is encoded in its precision (inverse covariance) matrix. Existing methods for multi-attribute differential graph estimation are based on a group lasso penalized loss function. In this paper, we consider a penalized D-trace loss function with non-convex [log-sum and smoothly clipped absolute deviation (SCAD)] penalties. Two proximal gradient descent methods are presented to optimize the objective function. Theoretical analysis establishing sufficient conditions for consistency in support recovery, convexity and estimation in high-dimensional settings is provided. We illustrate our approaches with numerical examples based on synthetic and real data. 

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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. Estimation of Differential Graphs from Time-Dependent Data

   https://doi.org/10.1109/CAMSAP58249.2023.10403521  

   Tugnait, Jitendra K (December 2023, IEEE)

   We consider the problem of estimating differences in two time series Gaussian graphical models (TSGGMs) which are known to have similar structure. The TSGGM structure is encoded in its inverse power spectral density (IPSD) just as the vector GGM structure is encoded in its precision (inverse covariance) matrix. Motivated by many applications, in existing works one is interested in estimating the difference in two precision matrices to characterize underlying changes in conditional dependencies of two sets of data comprised of independent and identically distributed observations. In this paper we consider estimation of the difference in two IPSD's to char-acterize underlying changes in conditional dependencies of two sets of time-dependent data. We analyze a group lasso penalized D-trace loss function approach in the frequency domain for differential graph learning, using Wirtinger calculus. An alternating direction method of multipliers (ADMM) algorithm is presented to optimize the objective function. Theoretical analysis establishing consistency of IPSD difference estimator in high-dimensional settings is presented. We illustrate our approach using a numerical example. 

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