  In the modern age of social media and networks, graph representations of
real-world phenomena have become an incredibly useful source to mine insights.
Often, we are interested in understanding how entities in a graph are
interconnected. The Graph Neural Network (GNN) has proven to be a very useful
tool in a variety of graph learning tasks including node classification, link
prediction, and edge classification. However, in most of these tasks, the graph
data we are working with may be noisy and may contain spurious edges. That is,
there is a lot of uncertainty associated with the underlying graph structure.
Recent approaches to modeling uncertainty have been to use a Bayesian framework
and view the graph as a random variable with probabilities associated with
model parameters. Introducing the Bayesian paradigm to graph-based models,
specifically for semi-supervised node classification, has been shown to yield
higher classification accuracies. However, the method of graph inference
proposed in recent work does not take into account the structure of the graph.
In this paper, we propose a novel algorithm called Bayesian Graph Convolutional
Network using Neighborhood Random Walk Sampling (BGCN-NRWS), which uses a
Markov Chain Monte Carlo (MCMC) based graph sampling algorithm utilizing graph
structure, reduces overfitting by using a variational inference layer, and
yields consistently competitive classification results compared to the
state-of-the-art in semi-supervised node classification.
