# Bayesian graph convolutional neural networks via tempered MCMC

arXiv: https://arxiv.org/abs/2104.08438 · HTML: https://mlsanity.com/paper/2104.08438/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 99 references that are in the map.
- First posted on arXiv 17 Apr 2021.

## Builds on (most cited first, 30 of 48)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [GaAN: Gated Attention Networks for Learning on Large and Spatiotemporal Graphs](https://mlsanity.com/paper/1803.07294/) (2018)
- [Bayesian Convolutional Neural Networks with Bernoulli Approximate Variational Inference](https://mlsanity.com/paper/1506.02158/) (2015)
- [Adaptive Graph Convolutional Neural Networks](https://mlsanity.com/paper/1801.03226/) (2018)
- [GraphGAN: Graph Representation Learning with Generative Adversarial Nets](https://mlsanity.com/paper/1711.08267/) (2017)

## Built on by (most cited first, 9 of 9)

- [Distribution Free Prediction Sets for Node Classification](https://mlsanity.com/paper/2211.14555/) (2022)
- [A review of ensemble learning and data augmentation models for class imbalanced problems: combination, implementation and evaluation](https://mlsanity.com/paper/2304.02858/) (2023)
- [A Survey on Epistemic (Model) Uncertainty in Supervised Learning: Recent Advances and Applications](https://mlsanity.com/paper/2111.01968/) (2021)
- [SMOTified-GAN for class imbalanced pattern classification problems](https://mlsanity.com/paper/2108.03235/) (2021)
- [Bayesian neural networks via MCMC: a Python-based tutorial](https://mlsanity.com/paper/2304.02595/) (2023)
- [Bayes-CATSI: A variational Bayesian deep learning framework for medical time series data imputation](https://mlsanity.com/paper/2410.01847/) (2024)
- [When narrower is better: the narrow width limit of Bayesian parallel branching neural networks](https://mlsanity.com/paper/2407.18807/) (2024)
- [Spatiotemporal deep learning models for detection of rapid intensification in cyclones](https://mlsanity.com/paper/2506.08397/) (2025)
- [Position: There Is No Free Bayesian Uncertainty Quantification](https://mlsanity.com/paper/2506.03670/) (2025)

## Abstract (arXiv)

Deep learning models, such as convolutional neural networks, have long been applied to image and multi-media tasks, particularly those with structured data. More recently, there has been more attention to unstructured data that can be represented via graphs. These types of data are often found in health and medicine, social networks, and research data repositories. Graph convolutional neural networks have recently gained attention in the field of deep learning that takes advantage of graph-based data representation with automatic feature extraction via convolutions. Given the popularity of these methods in a wide range of applications, robust uncertainty quantification is vital. This remains a challenge for large models and unstructured datasets. Bayesian inference provides a principled approach to uncertainty quantification of model parameters for deep learning models. Although Bayesian inference has been used extensively elsewhere, its application to deep learning remains limited due to the computational requirements of the Markov Chain Monte Carlo (MCMC) methods. Recent advances in parallel computing and advanced proposal schemes in MCMC sampling methods has opened the path for Bayesian deep learning. In this paper, we present Bayesian graph convolutional neural networks that employ tempered MCMC sampling with Langevin-gradient proposal distribution implemented via parallel computing. Our results show that the proposed method can provide accuracy similar to advanced optimisers while providing uncertainty quantification for key benchmark problems.