From Mice to Trains: Amortized Bayesian Inference on Graph Data

TL;DR

This paper adapts amortized Bayesian inference with neural networks to graph data, enabling scalable, permutation-invariant, likelihood-free posterior estimation for various graph parameters across multiple domains.

Contribution

It introduces a flexible, two-module neural pipeline combining permutation-invariant graph encoders with neural posterior estimators for efficient graph inference.

Findings

Multiple neural architectures evaluated as summary networks.

Performance assessed on synthetic and real-world biological and logistics data.

Achieved effective recovery and calibration of graph parameters.

Abstract

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.