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：图结构广泛出现于生物学、化学、社交与信息网络，以及交通物流等多个领域。针对图结构数据的推断需要满足置换不变性、能够适应不同规模与稀疏度，并能够捕捉复杂长程依赖关系的方法，这使得图参数的后验估计尤为困难。摊销贝叶斯推断是一种基于仿真的框架，它利用生成式神经网络实现快速、免似然函数的后验推断。我们将ABI方法适配于图数据以应对上述挑战，实现对节点级、边级和图级参数的推断。我们的方法将置换不变的图编码器与灵活的神经后验估计器结合，构建了一个双模块流程：摘要网络将属性图映射为固定长度的表示，而推断网络则近似参数的后验分布。在此框架下，多种神经架构均可作为摘要网络。本研究评估了多种架构，并在受控合成场景以及生物学和物流这两个现实领域，从参数恢复和校准两方面评估了它们的性能。