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.

翻译：图结构数据广泛存在于生物学、化学、社交网络与信息网络以及交通物流等不同领域。对图结构数据的推理需要满足置换不变性、跨不同规模与稀疏度的可扩展性，并具备捕捉复杂长程依赖关系的能力，这使得图参数的后验估计极具挑战性。摊销贝叶斯推断（ABI）是一种基于仿真的框架，利用生成式神经网络实现快速、无似然的后验推断。我们将ABI适配至图数据以应对这些挑战，对节点级、边级和图级参数进行推断。该方法通过双模块流水线将置换不变的图编码器与灵活的神经后验估计器相结合：摘要网络将属性图映射为固定长度表示，推断网络对参数的后验分布进行近似。在此框架下，多种神经架构均可作为摘要网络。本文对多种架构进行评测，在受控合成场景及生物学与物流两个真实领域案例中，从参数恢复与概率校准两个维度评估其性能。