  Semi-supervised learning (SSL) over graph-structured data emerges in many
network science applications. To efficiently manage learning over graphs,
variants of graph neural networks (GNNs) have been developed recently. By
succinctly encoding local graph structures and features of nodes,
state-of-the-art GNNs can scale linearly with the size of graph. Despite their
success in practice, most of existing methods are unable to handle graphs with
uncertain nodal attributes. Specifically whenever mismatches between training
and testing data distribution exists, these models fail in practice. Challenges
also arise due to distributional uncertainties associated with data acquired by
noisy measurements. In this context, a distributionally robust learning
framework is developed, where the objective is to train models that exhibit
quantifiable robustness against perturbations. The data distribution is
considered unknown, but lies within a Wasserstein ball centered around
empirical data distribution. A robust model is obtained by minimizing the worst
expected loss over this ball. However, solving the emerging functional
optimization problem is challenging, if not impossible. Advocating a strong
duality condition, we develop a principled method that renders the problem
tractable and efficiently solvable. Experiments assess the performance of the
proposed method.
