# Learning to Discover Sparse Graphical Models

arXiv: https://arxiv.org/abs/1605.06359 · HTML: https://mlsanity.com/paper/1605.06359/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 May 2016.

## Built on by (most cited first, 11 of 11)

- [Learning to Learn Graph Topologies](https://mlsanity.com/paper/2110.09807/) (2021)
- [Neural Graphical Models](https://mlsanity.com/paper/2210.00453/) (2022)
- [Diffusion Variational Autoencoder for Tackling Stochasticity in Multi-Step Regression Stock Price Prediction](https://mlsanity.com/paper/2309.00073/) (2023)
- [Learning to Infer Structures of Network Games](https://mlsanity.com/paper/2206.08119/) (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)
- [Sparse Graphical Linear Dynamical Systems](https://mlsanity.com/paper/2307.03210/) (2023)
- [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)
- [Learning Multi-Frequency Partial Correlation Graphs](https://mlsanity.com/paper/2311.15756/) (2023)
- [Multi-Source Wasserstein Distributionally Robust Graph Learning](https://mlsanity.com/paper/2608.19914/) (2026)

## Abstract (arXiv)

We consider structure discovery of undirected graphical models from observational data. Inferring likely structures from few examples is a complex task often requiring the formulation of priors and sophisticated inference procedures. Popular methods rely on estimating a penalized maximum likelihood of the precision matrix. However, in these approaches structure recovery is an indirect consequence of the data-fit term, the penalty can be difficult to adapt for domain-specific knowledge, and the inference is computationally demanding. By contrast, it may be easier to generate training samples of data that arise from graphs with the desired structure properties. We propose here to leverage this latter source of information as training data to learn a function, parametrized by a neural network that maps empirical covariance matrices to estimated graph structures. Learning this function brings two benefits: it implicitly models the desired structure or sparsity properties to form suitable priors, and it can be tailored to the specific problem of edge structure discovery, rather than maximizing data likelihood. Applying this framework, we find our learnable graph-discovery method trained on synthetic data generalizes well: identifying relevant edges in both synthetic and real data, completely unknown at training time. We find that on genetics, brain imaging, and simulation data we obtain performance generally superior to analytical methods.