  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 and robust 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 sampling, such as incorporating gradients has allowed
Bayesian deep learning methods to be implemented. In this paper, we present
Bayesian graph deep learning techniques that employ state-of-art methods such
as tempered MCMC sampling and advanced proposal schemes. Our results show that
Bayesian graph convolutional methods can provide accuracy similar to advanced
learning methods while providing a better alternative for robust uncertainty
quantification for key benchmark problems.
