# GLAD: Learning Sparse Graph Recovery

arXiv: https://arxiv.org/abs/1906.00271 · HTML: https://mlsanity.com/paper/1906.00271/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2019.

## Built on by (most cited first, 23 of 23)

- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Learning to Learn Graph Topologies](https://mlsanity.com/paper/2110.09807/) (2021)
- [Symbolic Learning to Optimize: Towards Interpretability and Scalability](https://mlsanity.com/paper/2203.06578/) (2022)
- [Neural Graphical Models](https://mlsanity.com/paper/2210.00453/) (2022)
- [Methods for Recovering Conditional Independence Graphs: A Survey](https://mlsanity.com/paper/2211.06829/) (2022)
- [uGLAD: Sparse graph recovery by optimizing deep unrolled networks](https://mlsanity.com/paper/2205.11610/) (2022)
- [Learning Graph Structure from Convolutional Mixtures](https://mlsanity.com/paper/2205.09575/) (2022)
- [Graph Structure Learning with Interpretable Bayesian Neural Networks](https://mlsanity.com/paper/2406.14786/) (2024)
- [Neural Graph Revealers](https://mlsanity.com/paper/2302.13582/) (2023)
- [Schur's Positive-Definite Network: Deep Learning in the SPD cone with structure](https://mlsanity.com/paper/2406.09023/) (2024)
- [Decentralized Statistical Inference with Unrolled Graph Neural Networks](https://mlsanity.com/paper/2104.01555/) (2021)
- [SF-SGL: Solver-Free Spectral Graph Learning from Linear Measurements](https://mlsanity.com/paper/2302.04384/) (2023)
- [Implicit Differentiation for Hyperparameter Tuning the Weighted Graphical Lasso](https://mlsanity.com/paper/2307.02130/) (2023)
- [Amortized Conditional Independence Testing](https://mlsanity.com/paper/2502.20925/) (2025)
- [pyGSL: A Graph Structure Learning Toolkit](https://mlsanity.com/paper/2211.03583/) (2022)
- [Are uGLAD? Time will tell!](https://mlsanity.com/paper/2303.11647/) (2023)
- [Knowledge Propagation over Conditional Independence Graphs](https://mlsanity.com/paper/2308.05857/) (2023)
- [Hypergraph-based multi-scale spatio-temporal graph convolution network for Time-Series anomaly detection](https://mlsanity.com/paper/2410.22256/) (2024)
- [Obstacle-aware Gaussian Process Regression](https://mlsanity.com/paper/2412.06160/) (2024)
- [LASE: Learned Adjacency Spectral Embeddings](https://mlsanity.com/paper/2412.17734/) (2024)
- [Graph Structure Learning with Privacy Guarantees for Open Graph Data](https://mlsanity.com/paper/2507.19116/) (2025)
- [Multi-Source Wasserstein Distributionally Robust Graph Learning](https://mlsanity.com/paper/2608.19914/) (2026)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)

## Abstract (arXiv)

Recovering sparse conditional independence graphs from data is a fundamental problem in machine learning with wide applications. A popular formulation of the problem is an ℓ1 regularized maximum likelihood estimation. Many convex optimization algorithms have been designed to solve this formulation to recover the graph structure. Recently, there is a surge of interest to learn algorithms directly based on data, and in this case, learn to map empirical covariance to the sparse precision matrix. However, it is a challenging task in this case, since the symmetric positive definiteness (SPD) and sparsity of the matrix are not easy to enforce in learned algorithms, and a direct mapping from data to precision matrix may contain many parameters. We propose a deep learning architecture, GLAD, which uses an Alternating Minimization (AM) algorithm as our model inductive bias, and learns the model parameters via supervised learning. We show that GLAD learns a very compact and effective model for recovering sparse graphs from data.