# GMNN: Graph Markov Neural Networks

arXiv: https://arxiv.org/abs/1905.06214 · HTML: https://mlsanity.com/paper/1905.06214/

## Key facts

- Cited by 82 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2019.

## Built on by (most cited first, 30 of 82)

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- [Topological Relational Learning on Graphs](https://mlsanity.com/paper/2110.15529/) (2021)
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- [Learning by Transference: Training Graph Neural Networks on Growing Graphs](https://mlsanity.com/paper/2106.03693/) (2021)
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- [Informative Pseudo-Labeling for Graph Neural Networks with Few Labels](https://mlsanity.com/paper/2201.07951/) (2022)
- [Understanding Non-linearity in Graph Neural Networks from the Bayesian-Inference Perspective](https://mlsanity.com/paper/2207.11311/) (2022)
- [A Unifying Generative Model for Graph Learning Algorithms: Label Propagation, Graph Convolutions, and Combinations](https://mlsanity.com/paper/2101.07730/) (2021)
- [GraphHop: An Enhanced Label Propagation Method for Node Classification](https://mlsanity.com/paper/2101.02326/) (2021)
- [VigDet: Knowledge Informed Neural Temporal Point Process for Coordination Detection on Social Media](https://mlsanity.com/paper/2110.15454/) (2021)
- [Neural Structured Prediction for Inductive Node Classification](https://mlsanity.com/paper/2204.07524/) (2022)
- [On the Correspondence Between Monotonic Max-Sum GNNs and Datalog](https://mlsanity.com/paper/2305.18015/) (2023)
- [Revisiting Bayesian Autoencoders with MCMC](https://mlsanity.com/paper/2104.05915/) (2021)
- [CARE: Certifiably Robust Learning with Reasoning via Variational Inference](https://mlsanity.com/paper/2209.05055/) (2022)
- [Bayesian graph convolutional neural networks via tempered MCMC](https://mlsanity.com/paper/2104.08438/) (2021)
- [Bures-Wasserstein Flow Matching for Graph Generation](https://mlsanity.com/paper/2506.14020/) (2025)
- [Graph Decoupling Attention Markov Networks for Semi-supervised Graph Node Classification](https://mlsanity.com/paper/2104.13718/) (2021)
- [Multi-task Self-distillation for Graph-based Semi-Supervised Learning](https://mlsanity.com/paper/2112.01174/) (2021)
- [Towards Digital Twin Oriented Modelling of Complex Networked Systems and Their Dynamics: A Comprehensive Survey](https://mlsanity.com/paper/2202.09363/) (2022)
- [Predicting cognitive scores with graph neural networks through sample selection learning](https://mlsanity.com/paper/2106.09408/) (2021)
- [Deeper-GXX: Deepening Arbitrary GNNs](https://mlsanity.com/paper/2110.13798/) (2021)
- [Tractable Probabilistic Graph Representation Learning with Graph-Induced Sum-Product Networks](https://mlsanity.com/paper/2305.10544/) (2023)
- [Calibrating and Improving Graph Contrastive Learning](https://mlsanity.com/paper/2101.11525/) (2021)

## Abstract (arXiv)

This paper studies semi-supervised object classification in relational data, which is a fundamental problem in relational data modeling. The problem has been extensively studied in the literature of both statistical relational learning (e.g. relational Markov networks) and graph neural networks (e.g. graph convolutional networks). Statistical relational learning methods can effectively model the dependency of object labels through conditional random fields for collective classification, whereas graph neural networks learn effective object representations for classification through end-to-end training. In this paper, we propose the Graph Markov Neural Network (GMNN) that combines the advantages of both worlds. A GMNN models the joint distribution of object labels with a conditional random field, which can be effectively trained with the variational EM algorithm. In the E-step, one graph neural network learns effective object representations for approximating the posterior distributions of object labels. In the M-step, another graph neural network is used to model the local label dependency. Experiments on object classification, link classification, and unsupervised node representation learning show that GMNN achieves state-of-the-art results.