  Predicting properties of nodes in a graph is an important problem with
applications in a variety of domains. Graph-based Semi-Supervised Learning
(SSL) methods aim to address this problem by labeling a small subset of the
nodes as seeds and then utilizing the graph structure to predict label scores
for the rest of the nodes in the graph. Recently, Graph Convolutional Networks
(GCNs) have achieved impressive performance on the graph-based SSL task. In
addition to label scores, it is also desirable to have confidence scores
associated with them. Unfortunately, confidence estimation in the context of
GCN has not been previously explored. We fill this important gap in this paper
and propose ConfGCN, which estimates labels scores along with their confidences
jointly in GCN-based setting. ConfGCN uses these estimated confidences to
determine the influence of one node on another during neighborhood aggregation,
thereby acquiring anisotropic capabilities. Through extensive analysis and
experiments on standard benchmarks, we find that ConfGCN is able to outperform
state-of-the-art baselines. We have made ConfGCN's source code available to
encourage reproducible research.
