  Recently, adaptive graph convolutional network based traffic prediction
methods, learning a latent graph structure from traffic data via various
attention-based mechanisms, have achieved impressive performance. However, they
are still limited to find a better description of spatial relationships between
traffic conditions due to: (1) ignoring the prior of the observed topology of
the road network; (2) neglecting the presence of negative spatial
relationships; and (3) lacking investigation on uncertainty of the graph
structure. In this paper, we propose a Bayesian Graph Convolutional Network
(BGCN) framework to alleviate these issues. Under this framework, the graph
structure is viewed as a random realization from a parametric generative model,
and its posterior is inferred using the observed topology of the road network
and traffic data. Specifically, the parametric generative model is comprised of
two parts: (1) a constant adjacency matrix which discovers potential spatial
relationships from the observed physical connections between roads using a
Bayesian approach; (2) a learnable adjacency matrix that learns a global shared
spatial correlations from traffic data in an end-to-end fashion and can model
negative spatial correlations. The posterior of the graph structure is then
approximated by performing Monte Carlo dropout on the parametric graph
structure. We verify the effectiveness of our method on five real-world
datasets, and the experimental results demonstrate that BGCN attains superior
performance compared with state-of-the-art methods.
