Graph Neural Networks Intersect Probabilistic Graphical Models: A Survey

TL;DR

This survey explores the intersection of Graph Neural Networks and Probabilistic Graphical Models, highlighting their complementary strengths and recent advances in combining these approaches for improved inference and learning on graph data.

Contribution

It provides a comprehensive overview of how GNNs and PGMs can mutually enhance each other, including methods for structured representation, explainability, and efficient inference.

Findings

GNNs can learn structured representations from PGMs.

PGMs can generate explainable predictions using GNNs.

The survey summarizes benchmark datasets and future research directions.

Abstract

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.