# Learning High-Dimensional Differential Graphs From Multi-Attribute Data

arXiv: https://arxiv.org/abs/2312.03761 · HTML: https://mlsanity.com/paper/2312.03761/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 46 references that are in the map.
- First posted on arXiv 5 Dec 2023.

## Builds on (most cited first, 9 of 9)

- [Node-Based Learning of Multiple Gaussian Graphical Models](https://mlsanity.com/paper/1303.5145/) (2013)
- [Differential Network Analysis via the Lasso Penalized D-Trace Loss](https://mlsanity.com/paper/1511.09188/) (2015)
- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)
- [A Direct Approach for Sparse Quadratic Discriminant Analysis](https://mlsanity.com/paper/1510.00084/) (2015)
- [Direct Estimation of Differential Functional Graphical Models](https://mlsanity.com/paper/1910.09701/) (2019)
- [FuDGE: A Method to Estimate a Functional Differential Graph in a High-Dimensional Setting](https://mlsanity.com/paper/2003.05402/) (2020)
- [Support Consistency of Direct Sparse-Change Learning in Markov Networks](https://mlsanity.com/paper/1407.0581/) (2014)
- [Testing for Differences in Gaussian Graphical Models: Applications to Brain Connectivity](https://mlsanity.com/paper/1512.08643/) (2015)
- [Direct Learning of Sparse Changes in Markov Networks by Density Ratio Estimation](https://mlsanity.com/paper/1304.6803/) (2013)

## Built on by (most cited first, 3 of 3)

- [Learning Multi-Attribute Differential Graphs with Non-Convex Penalties](https://mlsanity.com/paper/2505.09748/) (2025)
- [Multi-Attribute Graph Estimation with Sparse-Group Non-Convex Penalties](https://mlsanity.com/paper/2505.11984/) (2025)
- [Learning Conditional Independence Differential Graphs From Time-Dependent Data](https://mlsanity.com/paper/2512.06960/) (2025)

## Abstract (arXiv)

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.