  Missing node attributes is a common problem in real-world graphs. Graph
neural networks have been demonstrated power in graph representation learning
while their performance is affected by the completeness of graph information.
Most of them are not specified for missing-attribute graphs and fail to
leverage incomplete attribute information effectively. In this paper, we
propose an innovative node representation learning framework, Wasserstein Graph
Neural Network (WGNN), to mitigate the problem. To make the most of limited
observed attribute information and capture the uncertainty caused by missing
values, we express nodes as low-dimensional distributions derived from the
decomposition of the attribute matrix. Furthermore, we strengthen the
expressiveness of representations by developing a novel message passing schema
that aggregates distributional information from neighbors in the Wasserstein
space. We test WGNN in node classification tasks under two missing-attribute
cases on both synthetic and real-world datasets. In addition, we find WGNN
suitable to recover missing values and adapt them to tackle matrix completion
problems with graphs of users and items. Experimental results on both tasks
demonstrate the superiority of our method.
