# Multi-Attribute Graph Estimation with Sparse-Group Non-Convex Penalties

arXiv: https://arxiv.org/abs/2505.11984 · HTML: https://mlsanity.com/paper/2505.11984/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 32 references that are in the map.
- First posted on arXiv 17 May 2025.

## Builds on (most cited first, 7 of 7)

- [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)
- [Support recovery without incoherence: A case for nonconvex regularization](https://mlsanity.com/paper/1412.5632/) (2014)
- [FuDGE: A Method to Estimate a Functional Differential Graph in a High-Dimensional Setting](https://mlsanity.com/paper/2003.05402/) (2020)
- [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)
- [Learning High-Dimensional Differential Graphs From Multi-Attribute Data](https://mlsanity.com/paper/2312.03761/) (2023)

## Abstract (arXiv)

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.