  Graph Neural Networks (GNNs) have achieved great success in modeling
graph-structured data. However, recent works show that GNNs are vulnerable to
adversarial attacks which can fool the GNN model to make desired predictions of
the attacker. In addition, training data of GNNs can be leaked under membership
inference attacks. This largely hinders the adoption of GNNs in high-stake
domains such as e-commerce, finance and bioinformatics. Though investigations
have been made in conducting robust predictions and protecting membership
privacy, they generally fail to simultaneously consider the robustness and
membership privacy. Therefore, in this work, we study a novel problem of
developing robust and membership privacy-preserving GNNs. Our analysis shows
that Information Bottleneck (IB) can help filter out noisy information and
regularize the predictions on labeled samples, which can benefit robustness and
membership privacy. However, structural noises and lack of labels in node
classification challenge the deployment of IB on graph-structured data. To
mitigate these issues, we propose a novel graph information bottleneck
framework that can alleviate structural noises with neighbor bottleneck. Pseudo
labels are also incorporated in the optimization to minimize the gap between
the predictions on the labeled set and unlabeled set for membership privacy.
Extensive experiments on real-world datasets demonstrate that our method can
give robust predictions and simultaneously preserve membership privacy.
