Stability and Generalization of Hypergraph Collaborative Networks
Michael Ng Hanrui Wu Andy Yip
Graph neural networks have been shown to be very effective in utilizing
pairwise relationships across samples. Recently, there have been several
successful proposals to generalize graph neural networks to hypergraph neural
networks to exploit more complex relationships. In particular, the hypergraph
collaborative networks yield superior results compared to other hypergraph
neural networks for various semi-supervised learning tasks. The collaborative
network can provide high quality vertex embeddings and hyperedge embeddings
together by formulating them as a joint optimization problem and by using their
consistency in reconstructing the given hypergraph. In this paper, we aim to
establish the algorithmic stability of the core layer of the collaborative
network and provide generalization guarantees. The analysis sheds light on the
design of hypergraph filters in collaborative networks, for instance, how the
data and hypergraph filters should be scaled to achieve uniform stability of
the learning process. Some experimental results on real-world datasets are
presented to illustrate the theory.