# Estimation of partially known Gaussian graphical models with score-based structural priors

arXiv: https://arxiv.org/abs/2401.14340 · HTML: https://mlsanity.com/paper/2401.14340/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 57 references that are in the map.
- First posted on arXiv 25 Jan 2024.

## Builds on (most cited first, 12 of 12)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [Being Bayesian about Network Structure](https://mlsanity.com/paper/1301.3856/) (2013)
- [High-Dimensional Joint Estimation of Multiple Directed Gaussian Graphical Models](https://mlsanity.com/paper/1804.00778/) (2018)
- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)
- [High-dimensional Gaussian graphical model for network-linked data](https://mlsanity.com/paper/1907.02443/) (2019)
- [Bayesian inference for multiple Gaussian graphical models with application to metabolic association networks](https://mlsanity.com/paper/1603.06358/) (2016)
- [Bayesian topology inference on partially known networks from input-output pairs](https://mlsanity.com/paper/2309.06532/) (2023)
- [A Two-Part Mixed-Effects Modeling Framework For Analyzing Whole-Brain Network Data](https://mlsanity.com/paper/1409.7086/) (2014)
- [Gaussian graphical modeling for spectrometric data analysis](https://mlsanity.com/paper/2103.11666/) (2021)

## Built on by (most cited first, 2 of 2)

- [Fair GLASSO: Estimating Fair Graphical Models with Unbiased Statistical Behavior](https://mlsanity.com/paper/2406.09513/) (2024)
- [Polynomial Graphical Lasso: Learning Edges from Gaussian Graph-Stationary Signals](https://mlsanity.com/paper/2404.02621/) (2024)

## Abstract (arXiv)

We propose a novel algorithm for the support estimation of partially known Gaussian graphical models that incorporates prior information about the underlying graph. In contrast to classical approaches that provide a point estimate based on a maximum likelihood or a maximum a posteriori criterion using (simple) priors on the precision matrix, we consider a prior on the graph and rely on annealed Langevin diffusion to generate samples from the posterior distribution. Since the Langevin sampler requires access to the score function of the underlying graph prior, we use graph neural networks to effectively estimate the score from a graph dataset (either available beforehand or generated from a known distribution). Numerical experiments demonstrate the benefits of our approach.