Nonparametric Bayesian label prediction on a graph

TL;DR

This paper introduces a nonparametric Bayesian method for binary classification on graphs, leveraging graph Laplacian-based priors to incorporate graph structure, with demonstrated effectiveness on simulated and real datasets.

Contribution

It proposes a hierarchical Bayesian framework with novel priors that adapt to graph geometry, including a flexible partial conjugacy variant.

Findings

Effective classification on simulated data

Successful application to real-world datasets

Flexible prior models improve performance

Abstract

An implementation of a nonparametric Bayesian approach to solving binary classification problems on graphs is described. A hierarchical Bayesian approach with a randomly scaled Gaussian prior is considered. The prior uses the graph Laplacian to take into account the underlying geometry of the graph. A method based on a theoretically optimal prior and a more flexible variant using partial conjugacy are proposed. Two simulated data examples and two examples using real data are used in order to illustrate the proposed methods.