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1. 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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2. Graph Learning from Multi-Attribute Smooth Signals

   https://doi.org/10.1109/MLSP49062.2020.9231563  

   Tugnait, Jitendra K. (September 2020, 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP))

   null (Ed.)

   We consider the problem of estimating the structure of an undirected weighted graph underlying a set of smooth multi -attribute signals. Most existing methods for graph estimation are based on single-attribute models where one associates a scalar data variable with each node of the graph, and the problem is to infer the graph topology that captures the relationships between these variables. An example is image graphs for grayscale texture images for modeling dependence of a pixel on neighboring pixels. In multi-attribute graphical models, each node represents a vector, as for example, in color image graphs where one has three variables (RGB color components) per pixel node. In this paper, we extend the single attribute approach of Kalofolias (2016) to multi -attribute data. An alternating direction method of multipliers (ADMM) algorithm is presented to optimize the objective function to infer the graph topology. Numerical results based on synthetic as well as real data are presented. 

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3. 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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4. 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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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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