# Graph Neural Networks Intersect Probabilistic Graphical Models: A Survey

arXiv: https://arxiv.org/abs/2206.06089 · HTML: https://mlsanity.com/paper/2206.06089/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 50 references that are in the map.
- First posted on arXiv 24 May 2022.

## Builds on (most cited first, 27 of 27)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Explainability in Graph Neural Networks: A Taxonomic Survey](https://mlsanity.com/paper/2012.15445/) (2020)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Learning Discrete Structures for Graph Neural Networks](https://mlsanity.com/paper/1903.11960/) (2019)
- [Learning Deep Generative Models of Graphs](https://mlsanity.com/paper/1803.03324/) (2018)
- [PGM-Explainer: Probabilistic Graphical Model Explanations for Graph Neural Networks](https://mlsanity.com/paper/2010.05788/) (2020)
- [D-VAE: A Variational Autoencoder for Directed Acyclic Graphs](https://mlsanity.com/paper/1904.11088/) (2019)
- [Bayesian graph convolutional neural networks for semi-supervised classification](https://mlsanity.com/paper/1811.11103/) (2018)
- [GMNN: Graph Markov Neural Networks](https://mlsanity.com/paper/1905.06214/) (2019)
- [Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?](https://mlsanity.com/paper/2109.05641/) (2021)
- [Loopy Belief Propagation for Approximate Inference: An Empirical Study](https://mlsanity.com/paper/1301.6725/) (2013)
- [Directed Acyclic Graph Neural Networks](https://mlsanity.com/paper/2101.07965/) (2021)
- [Break the Ceiling: Stronger Multi-scale Deep Graph Convolutional Networks](https://mlsanity.com/paper/1906.02174/) (2019)
- [Neural Enhanced Belief Propagation on Factor Graphs](https://mlsanity.com/paper/2003.01998/) (2020)
- [Inference in Probabilistic Graphical Models by Graph Neural Networks](https://mlsanity.com/paper/1803.07710/) (2018)
- [Supervised Community Detection with Line Graph Neural Networks](https://mlsanity.com/paper/1705.08415/) (2017)
- [Neural Structured Prediction for Inductive Node Classification](https://mlsanity.com/paper/2204.07524/) (2022)
- [Semi-Supervised Node Classification on Graphs: Markov Random Fields vs. Graph Neural Networks](https://mlsanity.com/paper/2012.13085/) (2020)
- [Learning Node Representations from Noisy Graph Structures](https://mlsanity.com/paper/2012.02434/) (2020)

## Built on by (most cited first, 6 of 6)

- [The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challenges](https://mlsanity.com/paper/2407.09618/) (2024)
- [Joint Entity and Relation Extraction with Span Pruning and Hypergraph Neural Networks](https://mlsanity.com/paper/2310.17238/) (2023)
- [EnzymeFlow: Generating Reaction-specific Enzyme Catalytic Pockets through Flow Matching and Co-Evolutionary Dynamics](https://mlsanity.com/paper/2410.00327/) (2024)
- [Reaction-conditioned De Novo Enzyme Design with GENzyme](https://mlsanity.com/paper/2411.16694/) (2024)
- [On Addressing the Limitations of Graph Neural Networks](https://mlsanity.com/paper/2306.12640/) (2023)
- [Predicting Cascade Failures in Interdependent Urban Infrastructure Networks](https://mlsanity.com/paper/2503.02890/) (2025)

## Abstract (arXiv)

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.