# uGLAD: Sparse graph recovery by optimizing deep unrolled networks

arXiv: https://arxiv.org/abs/2205.11610 · HTML: https://mlsanity.com/paper/2205.11610/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 52 references that are in the map.
- First posted on arXiv 23 May 2022.

## Builds on (most cited first, 13 of 13)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Stochastic Video Generation with a Learned Prior](https://mlsanity.com/paper/1802.07687/) (2018)
- [A Tutorial on Learning With Bayesian Networks](https://mlsanity.com/paper/2002.00269/) (2020)
- [Network Inference via the Time-Varying Graphical Lasso](https://mlsanity.com/paper/1703.01958/) (2017)
- [Node-Based Learning of Multiple Gaussian Graphical Models](https://mlsanity.com/paper/1303.5145/) (2013)
- [Learning to Learn Graph Topologies](https://mlsanity.com/paper/2110.09807/) (2021)
- [RNA Secondary Structure Prediction By Learning Unrolled Algorithms](https://mlsanity.com/paper/2002.05810/) (2020)
- [GLAD: Learning Sparse Graph Recovery](https://mlsanity.com/paper/1906.00271/) (2019)
- [Diverse Video Generation using a Gaussian Process Trigger](https://mlsanity.com/paper/2107.04619/) (2021)
- [Graphical LASSO Based Model Selection for Time Series](https://mlsanity.com/paper/1410.1184/) (2014)
- [Learning to Discover Sparse Graphical Models](https://mlsanity.com/paper/1605.06359/) (2016)
- [Cooperative neural networks (CoNN): Exploiting prior independence structure for improved classification](https://mlsanity.com/paper/1906.00291/) (2019)

## Built on by (most cited first, 6 of 6)

- [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)
- [Neural Graph Revealers](https://mlsanity.com/paper/2302.13582/) (2023)
- [Federated Learning with Neural Graphical Models](https://mlsanity.com/paper/2309.11680/) (2023)
- [Are uGLAD? Time will tell!](https://mlsanity.com/paper/2303.11647/) (2023)
- [Obstacle-aware Gaussian Process Regression](https://mlsanity.com/paper/2412.06160/) (2024)

## Abstract (arXiv)

Probabilistic Graphical Models (PGMs) are generative models of complex systems. They rely on conditional independence assumptions between variables to learn sparse representations which can be visualized in a form of a graph. Such models are used for domain exploration and structure discovery in poorly understood domains. This work introduces a novel technique to perform sparse graph recovery by optimizing deep unrolled networks. Assuming that the input data X∈ℝM× D comes from an underlying multivariate Gaussian distribution, we apply a deep model on X that outputs the precision matrix hatTheta, which can also be interpreted as the adjacency matrix. Our model, uGLAD, builds upon and extends the state-of-the-art model GLAD to the unsupervised setting. The key benefits of our model are (1) uGLAD automatically optimizes sparsity-related regularization parameters leading to better performance than existing algorithms. (2) We introduce multi-task learning based `consensus' strategy for robust handling of missing data in an unsupervised setting. We evaluate model results on synthetic Gaussian data, non-Gaussian data generated from Gene Regulatory Networks, and present a case study in anaerobic digestion.