A Bayesian reassessment of nearest-neighbour classification

TL;DR

This paper redefines the k-nearest-neighbour classification as a Bayesian model, providing new computational tools and demonstrating the approach's effectiveness and limitations through benchmark datasets.

Contribution

It establishes a clear probabilistic framework for k-NN, introduces Bayesian inference methods, and compares their performance with traditional approximations.

Findings

Bayesian model offers a rigorous foundation for k-NN.

Perfect sampling improves inference accuracy.

Pseudo-likelihood approximation has notable limitations.

Abstract

The k-nearest-neighbour procedure is a well-known deterministic method used in supervised classification. This paper proposes a reassessment of this approach as a statistical technique derived from a proper probabilistic model; in particular, we modify the assessment made in a previous analysis of this method undertaken by Holmes and Adams (2002,2003), and evaluated by Manocha and Girolami (2007), where the underlying probabilistic model is not completely well-defined. Once a clear probabilistic basis for the k-nearest-neighbour procedure is established, we derive computational tools for conducting Bayesian inference on the parameters of the corresponding model. In particular, we assess the difficulties inherent to pseudo-likelihood and to path sampling approximations of an intractable normalising constant, and propose a perfect sampling strategy to implement a correct MCMC sampler associated with our model. If perfect sampling is not available, we suggest using a Gibbs sampling approximation. Illustrations of the performance of the corresponding Bayesian classifier are provided for several benchmark datasets, demonstrating in particular the limitations of the pseudo-likelihood approximation in this set-up.