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

Martín Sevilla, Antonio G. Marques, Santiago Segarra
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:1558-1566, 2024.

Abstract

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 maximum a posteriori approach 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 in different setups demonstrate the benefits of our approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-sevilla24a, title = {Estimation of partially known {G}aussian graphical models with score-based structural priors}, author = {Sevilla, Mart\'{i}n and G. Marques, Antonio and Segarra, Santiago}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {1558--1566}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/sevilla24a/sevilla24a.pdf}, url = {https://proceedings.mlr.press/v238/sevilla24a.html}, abstract = {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 maximum a posteriori approach 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 in different setups demonstrate the benefits of our approach.} }
Endnote
%0 Conference Paper %T Estimation of partially known Gaussian graphical models with score-based structural priors %A Martín Sevilla %A Antonio G. Marques %A Santiago Segarra %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-sevilla24a %I PMLR %P 1558--1566 %U https://proceedings.mlr.press/v238/sevilla24a.html %V 238 %X 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 maximum a posteriori approach 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 in different setups demonstrate the benefits of our approach.
APA
Sevilla, M., G. Marques, A. & Segarra, S.. (2024). Estimation of partially known Gaussian graphical models with score-based structural priors. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:1558-1566 Available from https://proceedings.mlr.press/v238/sevilla24a.html.

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