  Graph Convolutional Network (GCN) has exhibited strong empirical performance
in many real-world applications. The vast majority of existing works on GCN
primarily focus on the accuracy while ignoring how confident or uncertain a GCN
is with respect to its predictions. Despite being a cornerstone of trustworthy
graph mining, uncertainty quantification on GCN has not been well studied and
the scarce existing efforts either fail to provide deterministic quantification
or have to change the training procedure of GCN by introducing additional
parameters or architectures. In this paper, we propose the first
frequentist-based approach named JuryGCN in quantifying the uncertainty of GCN,
where the key idea is to quantify the uncertainty of a node as the width of
confidence interval by a jackknife estimator. Moreover, we leverage the
influence functions to estimate the change in GCN parameters without
re-training to scale up the computation. The proposed JuryGCN is capable of
quantifying uncertainty deterministically without modifying the GCN
architecture or introducing additional parameters. We perform extensive
experimental evaluation on real-world datasets in the tasks of both active
learning and semi-supervised node classification, which demonstrate the
efficacy of the proposed method.
