Graphs are a powerful data structure to represent relational data and are widely used to describe complex real-world data structures. Probabilistic Graphical Models (PGMs) have been well-developed in the past years to mathematically model real-world scenarios in compact graphical representations of distributions of variables. Graph Neural Networks (GNNs) are new inference methods developed in recent years and are attracting growing attention due to their effectiveness and flexibility in solving inference and learning problems over graph-structured data. These two powerful approaches have different advantages in capturing relations from observations and how they conduct message passing, and they can benefit each other in various tasks. In this survey, we broadly study the intersection of GNNs and PGMs. Specifically, we first discuss how GNNs can benefit from learning structured representations in PGMs, generate explainable predictions by PGMs, and how PGMs can infer object relationships. Then we discuss how GNNs are implemented in PGMs for more efficient inference and structure learning. In the end, we summarize the benchmark datasets used in recent studies and discuss promising future directions.

翻译：图是一种强大的数据结构，用于表示关系型数据，并广泛应用于描述复杂现实世界的数据结构。概率图模型（PGMs）经过多年发展，能够以紧凑的变量分布图形化表示来数学建模现实场景。图神经网络（GNNs）是近年来发展的新型推理方法，因其在解决图结构数据上的推理与学习问题中展现的高效性与灵活性而日益受到关注。这两种强大方法在从观测中捕捉关系及执行消息传递方面具有不同优势，且能在多种任务中相互促进。本综述全面研究了GNNs与PGMs的交叉领域。具体而言，我们首先探讨GNNs如何从PGMs的结构化表示学习中获益、如何通过PGMs生成可解释预测，以及PGMs如何推断目标关系。随后讨论GNNs如何被嵌入PGMs以实现更高效的推理与结构学习。最后，我们总结了近期研究采用的基准数据集，并展望了有前景的未来方向。