# Bayesian topology inference on partially known networks from input-output pairs

arXiv: https://arxiv.org/abs/2309.06532 · HTML: https://mlsanity.com/paper/2309.06532/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2023.

## Built on by (most cited first, 3 of 3)

- [Graph Structure Learning with Interpretable Bayesian Neural Networks](https://mlsanity.com/paper/2406.14786/) (2024)
- [Estimation of partially known Gaussian graphical models with score-based structural priors](https://mlsanity.com/paper/2401.14340/) (2024)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)

## Abstract (arXiv)

We propose a sampling algorithm to perform system identification from a set of input-output graph signal pairs. The dynamics of the systems we study are given by a partially known adjacency matrix and a generic parametric graph filter of unknown parameters. The methodology we employ is built upon the principles of annealed Langevin diffusion. This enables us to draw samples from the posterior distribution instead of following the classical approach of point estimation using maximum likelihood. We investigate how to harness the prior information inherent in a dataset of graphs of different sizes through the utilization of graph neural networks. We demonstrate, via numerical experiments involving both real-world and synthetic networks, that integrating prior knowledge into the estimation process enhances estimation performance.