Stability and Generalization of Hypergraph Collaborative Networks

TL;DR

This paper analyzes the stability and generalization properties of hypergraph collaborative networks, providing theoretical guarantees and insights into their design, supported by experiments on real-world datasets.

Contribution

It establishes the algorithmic stability of the core layer of hypergraph collaborative networks and offers guidelines for designing hypergraph filters for better generalization.

Findings

The core layer of the network is proven to be stable under certain conditions.

Hypergraph filters should be scaled appropriately to ensure stability.

Experimental results support the theoretical stability guarantees.

Abstract

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.