Bayesian graph convolutional neural networks via tempered MCMC

TL;DR

This paper introduces Bayesian graph convolutional neural networks utilizing tempered MCMC with Langevin-gradient proposals, enabling effective uncertainty quantification in graph-based deep learning models with competitive accuracy.

Contribution

The paper presents a novel Bayesian GCN framework using tempered MCMC with Langevin-gradient proposals, leveraging parallel computing for efficient uncertainty estimation.

Findings

Achieves accuracy comparable to advanced optimizers.

Provides uncertainty quantification for benchmark problems.

Demonstrates scalability with parallel computing.

Abstract

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.