# Learning Multi-Attribute Differential Graphs with Non-Convex Penalties

arXiv: https://arxiv.org/abs/2505.09748 · HTML: https://mlsanity.com/paper/2505.09748/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 50 references that are in the map.
- First posted on arXiv 14 May 2025.

## Builds on (most cited first, 15 of 15)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Regularized M-estimators with nonconvexity: Statistical and algorithmic theory for local optima](https://mlsanity.com/paper/1305.2436/) (2013)
- [A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems](https://mlsanity.com/paper/1303.4434/) (2013)
- [Support recovery without incoherence: A case for nonconvex regularization](https://mlsanity.com/paper/1412.5632/) (2014)
- [Structured Graph Learning Via Laplacian Spectral Constraints](https://mlsanity.com/paper/1909.11594/) (2019)
- [Vector-Valued Graph Trend Filtering with Non-Convex Penalties](https://mlsanity.com/paper/1905.12692/) (2019)
- [Differential Network Analysis via the Lasso Penalized D-Trace Loss](https://mlsanity.com/paper/1511.09188/) (2015)
- [A Direct Approach for Sparse Quadratic Discriminant Analysis](https://mlsanity.com/paper/1510.00084/) (2015)
- [FuDGE: A Method to Estimate a Functional Differential Graph in a High-Dimensional Setting](https://mlsanity.com/paper/2003.05402/) (2020)
- [Testing for Differences in Gaussian Graphical Models: Applications to Brain Connectivity](https://mlsanity.com/paper/1512.08643/) (2015)
- [Efficient Learning with a Family of Nonconvex Regularizers by Redistributing Nonconvexity](https://mlsanity.com/paper/1606.03841/) (2016)
- [Sparse Graph Learning Under Laplacian-Related Constraints](https://mlsanity.com/paper/2111.08161/) (2021)
- [Sparse-Group Log-Sum Penalized Graphical Model Learning For Time Series](https://mlsanity.com/paper/2204.13824/) (2022)
- [Efficient Graph Laplacian Estimation by Proximal Newton](https://mlsanity.com/paper/2302.06434/) (2023)
- [Learning High-Dimensional Differential Graphs From Multi-Attribute Data](https://mlsanity.com/paper/2312.03761/) (2023)

## Built on by (most cited first, 1 of 1)

- [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 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.