Classification using log Gaussian Cox processes

TL;DR

This paper explores the log Gaussian Cox process for classification, demonstrating its theoretical properties, efficient computation, connections to classical methods, and effectiveness in supervised and semi-supervised learning scenarios.

Contribution

It introduces a novel log Gaussian Cox process classification model, analyzes its properties, links it to classical methods, and extends it to semi-supervised learning with graph min-cut inference.

Findings

Linear scaling of predictive probability with training size

Effective extension to semi-supervised learning

Good empirical performance on multiple datasets

Abstract

McCullagh and Yang (2006) suggest a family of classification algorithms based on Cox processes. We further investigate the log Gaussian variant which has a number of appealing properties. Conditioned on the covariates, the distribution over labels is given by a type of conditional Markov random field. In the supervised case, computation of the predictive probability of a single test point scales linearly with the number of training points and the multiclass generalization is straightforward. We show new links between the supervised method and classical nonparametric methods. We give a detailed analysis of the pairwise graph representable Markov random field, which we use to extend the model to semi-supervised learning problems, and propose an inference method based on graph min-cuts. We give the first experimental analysis on supervised and semi-supervised datasets and show good empirical performance.