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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. Multi-Attribute Graph Estimation With Sparse-Group Non-Convex Penalties

   https://doi.org/10.1109/ACCESS.2025.3566959  

   Tugnait, Jitendra K (January 2025, IEEE Access)

   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 provide a unified theoretical analysis of multi-attribute graph learning using a penalized log-likelihood objective function. We consider both convex (sparse-group lasso) and sparse-group non-convex (log-sum and smoothly clipped absolute deviation (SCAD) penalties) penalty/regularization functions. An alternating direction method of multipliers (ADMM) approach coupled with local linear approximation to non-convex penalties is presented for optimization of the objective function. For non-convex penalties, theoretical analysis establishing local consistency in support recovery, local convexity and precision matrix estimation in high-dimensional settings is provided under two sets of sufficient conditions: with and without some irrepresentability conditions. We illustrate our approaches using both synthetic and real-data numerical examples. In the synthetic data examples the sparse-group log-sum penalized objective function significantly outperformed the lasso penalized as well as SCAD penalized objective functions with F1 -score and Hamming distance as performance metrics. 

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3. On Sparse High-Dimensional Graph Estimation from Multi-Attribute Data

   https://doi.org/10.1109/IEEECONF60004.2024.10942781  

   Tugnait, Jitendra K (October 2024, IEEE)

   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 provide a unified theoretical analysis of multi-attribute graph learning using a penalized log-likelihood objective function. We consider both convex (sparse-group lasso) and non-convex (log-sum and SCAD group penalties) penalty/regularization functions. We establish sufficient conditions in a high-dimensional setting for consistency (convergence of the precision matrix to true value in the Frobenius norm), local convexity when using non-convex penalties, and graph recovery. We do not impose any incoherence or irrepresentability condition for our convergence results. 

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4. Conditional Independence Graph Estimation from Multi-Attribute Dependent Time Series

   https://doi.org/10.1109/MLSP58920.2024.10734734  

   Tugnait, Jitendra K (September 2024, IEEE)

   Estimation of the conditional independence graph (CIG) of high-dimensional multivariate Gaussian time series from multi-attribute data is considered. All existing methods for graph estimation for such data are based on single-attribute models where one associates a scalar time series with each node. In multi-attribute graphical models, each node represents a random vector or vector time series. In this paper we provide a unified theoretical analysis of multi-attribute graph learning for dependent time series using a penalized log-likelihood objective function. We consider both convex (sparse-group lasso) and non-convex (log-sum and SCAD group penalties) penalty/regularization functions. We establish sufficient conditions in a high-dimensional setting for consistency (convergence of the inverse power spectral density to true value in the Frobenius norm), local convexity when using non-convex penalties, and graph recovery. We illustrate our approach using numerical examples utilizing both synthetic and real data. 

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5. 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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