Gaussian Processes on Hypergraphs
This work addresses the problem of modeling complex relational data with hypergraphs for researchers in machine learning and statistics, offering a novel method but with incremental extensions to existing GP techniques.
The authors introduced a Matern Gaussian process on hypergraph vertices to estimate regression models with correlation and uncertainty informed by hypergraph structure, and demonstrated its utility on three real-world problems including political party classification, movie review matrix factorization, and animal hypergraph embedding.
We derive a Matern Gaussian process (GP) on the vertices of a hypergraph. This enables estimation of regression models of observed or latent values associated with the vertices, in which the correlation and uncertainty estimates are informed by the hypergraph structure. We further present a framework for embedding the vertices of a hypergraph into a latent space using the hypergraph GP. Finally, we provide a scheme for identifying a small number of representative inducing vertices that enables scalable inference through sparse GPs. We demonstrate the utility of our framework on three challenging real-world problems that concern multi-class classification for the political party affiliation of legislators on the basis of voting behaviour, probabilistic matrix factorisation of movie reviews, and embedding a hypergraph of animals into a low-dimensional latent space.