# Inference in Probabilistic Graphical Models by Graph Neural Networks

arXiv: https://arxiv.org/abs/1803.07710 · HTML: https://mlsanity.com/paper/1803.07710/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2018.

## Built on by (most cited first, 30 of 38)

- [The Expressive Power of Graph Neural Networks: A Survey](https://mlsanity.com/paper/2308.08235/) (2023)
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- [Joint Entity and Relation Extraction with Span Pruning and Hypergraph Neural Networks](https://mlsanity.com/paper/2310.17238/) (2023)
- [Message Passing Meets Graph Neural Networks: A New Paradigm for Massive MIMO Systems](https://mlsanity.com/paper/2302.06896/) (2023)
- [Constrained Layout Generation with Factor Graphs](https://mlsanity.com/paper/2404.00385/) (2024)
- [Safety-Oriented Pedestrian Motion and Scene Occupancy Forecasting](https://mlsanity.com/paper/2101.02385/) (2021)
- [Graph Neural Networks Intersect Probabilistic Graphical Models: A Survey](https://mlsanity.com/paper/2206.06089/) (2022)
- [Neural Enhanced Belief Propagation for Cooperative Localization](https://mlsanity.com/paper/2105.12903/) (2021)
- [GCEPNet: Graph Convolution-Enhanced Expectation Propagation for Massive MIMO Detection](https://mlsanity.com/paper/2404.14886/) (2024)
- [Are Large-Language Models Graph Algorithmic Reasoners?](https://mlsanity.com/paper/2410.22597/) (2024)
- [Towards Better Generalization with Flexible Representation of Multi-Module Graph Neural Networks](https://mlsanity.com/paper/2209.06589/) (2022)
- [Mapping the Internet: Modelling Entity Interactions in Complex Heterogeneous Networks](https://mlsanity.com/paper/2104.09650/) (2021)
- [Graph Belief Propagation Networks](https://mlsanity.com/paper/2106.03033/) (2021)
- [Learning Dynamics and Structure of Complex Systems Using Graph Neural Networks](https://mlsanity.com/paper/2202.10996/) (2022)
- [Graph Neural Network Aided MU-MIMO Detectors](https://mlsanity.com/paper/2206.09381/) (2022)
- [Neural Network Approximators for Marginal MAP in Probabilistic Circuits](https://mlsanity.com/paper/2402.03621/) (2024)
- [Differentiable Cluster Graph Neural Network](https://mlsanity.com/paper/2405.16185/) (2024)
- [Equivariant Neural Network for Factor Graphs](https://mlsanity.com/paper/2109.14218/) (2021)
- [IBIA: Bayesian Inference via Incremental Build-Infer-Approximate operations on Clique Trees](https://mlsanity.com/paper/2202.12003/) (2022)
- [Inferring Inference](https://mlsanity.com/paper/2310.03186/) (2023)
- [Learning in Deep Factor Graphs with Gaussian Belief Propagation](https://mlsanity.com/paper/2311.14649/) (2023)
- [Modeling Graph Node Correlations with Neighbor Mixture Models](https://mlsanity.com/paper/2103.15966/) (2021)
- [Generalization of graph network inferences in higher-order graphical models](https://mlsanity.com/paper/2107.05729/) (2021)
- [DAGSurv: Directed Acyclic Graph Based Survival Analysis Using Deep Neural Networks](https://mlsanity.com/paper/2111.01482/) (2021)
- [Knowledge-Integrated Informed AI for National Security](https://mlsanity.com/paper/2202.03188/) (2022)
- [Edge Graph Neural Networks for Massive MIMO Detection](https://mlsanity.com/paper/2206.06979/) (2022)
- [Local Message Passing on Frustrated Systems](https://mlsanity.com/paper/2306.01494/) (2023)

## Abstract (arXiv)

A fundamental computation for statistical inference and accurate decision-making is to compute the marginal probabilities or most probable states of task-relevant variables. Probabilistic graphical models can efficiently represent the structure of such complex data, but performing these inferences is generally difficult. Message-passing algorithms, such as belief propagation, are a natural way to disseminate evidence amongst correlated variables while exploiting the graph structure, but these algorithms can struggle when the conditional dependency graphs contain loops. Here we use Graph Neural Networks (GNNs) to learn a message-passing algorithm that solves these inference tasks. We first show that the architecture of GNNs is well-matched to inference tasks. We then demonstrate the efficacy of this inference approach by training GNNs on a collection of graphical models and showing that they substantially outperform belief propagation on loopy graphs. Our message-passing algorithms generalize out of the training set to larger graphs and graphs with different structure.