# Estimation of Graphical Models through Structured Norm Minimization

arXiv: https://arxiv.org/abs/1609.09010 · HTML: https://mlsanity.com/paper/1609.09010/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2016.

## Built on by (most cited first, 10 of 10)

- [Learning Graphical Factor Models with Riemannian Optimization](https://mlsanity.com/paper/2210.11950/) (2022)
- [Query-Aware Flow Diffusion for Graph-Based RAG with Retrieval Guarantees](https://mlsanity.com/paper/2605.18775/) (2026)
- [Fairness-Aware Estimation of Graphical Models](https://mlsanity.com/paper/2408.17396/) (2024)
- [Leveraging Low-rank Factorizations of Conditional Correlation Matrices in Graph Learning](https://mlsanity.com/paper/2506.10628/) (2025)
- [Multilayer Graph Clustering with Optimized Node Embedding](https://mlsanity.com/paper/2103.16534/) (2021)
- [The non-overlapping statistical approximation to overlapping group lasso](https://mlsanity.com/paper/2211.09221/) (2022)
- [Learning the hub graphical Lasso model with the structured sparsity via an efficient algorithm](https://mlsanity.com/paper/2308.08852/) (2023)
- [Clusterpath Gaussian Graphical Modeling](https://mlsanity.com/paper/2407.00644/) (2024)
- [Clustering Alzheimer's Disease Subtypes via Similarity Learning and Graph Diffusion](https://mlsanity.com/paper/2410.03937/) (2024)
- [Co-Hub Node Based Multiview Graph Learning with Theoretical Guarantees](https://mlsanity.com/paper/2512.12435/) (2025)

## Abstract (arXiv)

Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of em sparsity of the underlying model. In this paper, we study the problem of estimating such models exhibiting a more intricate structure comprising simultaneously of em sparse, structured sparse and em dense components. Such structures naturally arise in several scientific fields, including molecular biology, finance, and political science. We introduce a general framework based on a novel structured norm that enables us to estimate such complex structures from high-dimensional data. The resulting optimization problem is convex and we introduce a linearized multi-block alternating direction method of multipliers (ADMM) algorithm to solve it efficiently. We illustrate the superior performance of the proposed framework on a number of synthetic data sets generated from both random and structured networks. Further, we apply the method to a number of real data sets and discuss the results.