Estimation of Gaussian Graphical Models Using Learned Graph Priors
| dc.contributor.advisor | Segarra, Santiago | en_US |
| dc.creator | Sevilla, Martin | en_US |
| dc.date.accessioned | 2024-08-30T18:30:17Z | en_US |
| dc.date.available | 2024-08-30T18:30:17Z | en_US |
| dc.date.created | 2024-08 | en_US |
| dc.date.issued | 2024-08-06 | en_US |
| dc.date.submitted | August 2024 | en_US |
| dc.date.updated | 2024-08-30T18:30:17Z | en_US |
| dc.description.abstract | We propose a novel algorithm for estimating Gaussian graphical models incorporating prior information about the underlying graph. Classical approaches generally propose optimization problems with sparsity penalties as prior information. While efficient, these approaches do not allow using involved prior distributions and force us to incorporate the prior information on the precision matrix rather than on its support. In this work, we investigate how to estimate the graph of a Gaussian graphical model by introducing any prior distribution directly on the graph structure. We use graph neural networks to learn the score function of any graph prior and then leverage Langevin diffusion to generate samples from the posterior distribution. We study the estimation of both partially known and entirely unknown graphical models and prove that our proposed estimator is consistent in both scenarios. Finally, numerical experiments using synthetic and real-world graphs demonstrate the benefits of our approach. | en_US |
| dc.format.mimetype | application/pdf | en_US |
| dc.identifier.citation | Sevilla, Martin. Estimation of Gaussian Graphical Models Using Learned Graph Priors. (2024). Masters thesis, Rice University. https://hdl.handle.net/1911/117826 | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/117826 | en_US |
| dc.language.iso | eng | en_US |
| dc.rights | Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder. | en_US |
| dc.subject | Covariance selection | en_US |
| dc.subject | graphical models | en_US |
| dc.subject | network inference | en_US |
| dc.subject | Langevin dynamics | en_US |
| dc.title | Estimation of Gaussian Graphical Models Using Learned Graph Priors | en_US |
| dc.type | Thesis | en_US |
| dc.type.material | Text | en_US |
| thesis.degree.department | Electrical and Computer Engineering | en_US |
| thesis.degree.discipline | Engineering | en_US |
| thesis.degree.grantor | Rice University | en_US |
| thesis.degree.level | Masters | en_US |
| thesis.degree.name | Master of Science | en_US |
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