Deep Learning over Hypergraphs

Abstract

Graphs have been extensively used for modelling real-world network datasets, however, they are restricted to pairwise relationships, i.e., each edge connects exactly two vertices. Hypergraphs relax the notion of edges to connect arbitrary numbers of vertices. Hypergraphs provide a mathematical foundation for understanding and learning from large amounts of real-world data. State-of-the-art techniques for learning vertex representations from graph data with pairwise relationships use graph-based deep models such as graph neural networks. A prominent observation that inspires this thesis is that neural networks are still underexplored for hypergraph data with group-wise relationships. The main challenges involved are (a) handling the relational nature of hypergraph data and (b) dealing with group relations where a group contains an arbitrary number of vertices rather than a fixed number. In this work, we tackle these challenges and fill important research gaps through the following contributions. Deep Learning for Hypergraph Vertex-Level Predictions We explore connections between graph neural networks (GNNs) and spectral hypergraph theory and also connections between GNNs and optimal transport. These connections lead to novel vertex representation learning methods over hypergraphs. We demonstrate the effectiveness of the proposed methods on vertex property prediction. Deep Learning for Hypergraph Link Prediction We propose novel hypergraph scoring functions for link prediction. In contrast to existing methods, our proposed methods can be applied for predicting missing links in real-world hypergraphs in which hyperedges need not represent similarity. Deep Learning for Multi-Relational and Recursive Hypergraphs We unify various methods for message passing on different structures (e.g., hypergraphs, heterogeneous graphs, etc.) into a single framework. We next propose novel extensions of these methods and demonstrate the effectiveness for reasoning over knowledge bases