  We propose a framework that lifts the capabilities of graph convolutional
networks (GCNs) to scenarios where no input graph is given and increases their
robustness to adversarial attacks. We formulate a joint probabilistic model
that considers a prior distribution over graphs along with a GCN-based
likelihood and develop a stochastic variational inference algorithm to estimate
the graph posterior and the GCN parameters jointly. To address the problem of
propagating gradients through latent variables drawn from discrete
distributions, we use their continuous relaxations known as Concrete
distributions. We show that, on real datasets, our approach can outperform
state-of-the-art Bayesian and non-Bayesian graph neural network algorithms on
the task of semi-supervised classification in the absence of graph data and
when the network structure is subjected to adversarial perturbations.
