From Mice to Trains: Amortized Bayesian Inference on Graph Data
This work addresses the problem of scalable and permutation-invariant posterior estimation on graphs for researchers and practitioners in fields like biology and logistics, representing an incremental advancement by applying existing ABI methods to graph data.
The authors tackled the challenge of performing Bayesian inference on graph-structured data by adapting Amortized Bayesian Inference (ABI) to handle node-, edge-, and graph-level parameters, achieving improved performance in recovery and calibration on synthetic and real-world datasets from biology and logistics.
Graphs arise across diverse domains, from biology and chemistry to social and information networks, as well as in transportation and logistics. Inference on graph-structured data requires methods that are permutation-invariant, scalable across varying sizes and sparsities, and capable of capturing complex long-range dependencies, making posterior estimation on graph parameters particularly challenging. Amortized Bayesian Inference (ABI) is a simulation-based framework that employs generative neural networks to enable fast, likelihood-free posterior inference. We adapt ABI to graph data to address these challenges to perform inference on node-, edge-, and graph-level parameters. Our approach couples permutation-invariant graph encoders with flexible neural posterior estimators in a two-module pipeline: a summary network maps attributed graphs to fixed-length representations, and an inference network approximates the posterior over parameters. In this setting, several neural architectures can serve as the summary network. In this work we evaluate multiple architectures and assess their performance on controlled synthetic settings and two real-world domains - biology and logistics - in terms of recovery and calibration.