2008/02/10 by Lionel Cucala, Jean-Michel Marin, Jean‐Michel Marin +7 · 1 citation
Computer Science · Mathematics · #Anomaly Detection Techniques and Applications #Bayesian Methods and Mixture Models #Statistical Methods and Inference #math.ST #stat.CO #stat.TH
paper · pdf · doi:10.48550/arxiv.0802.1357
arxiv created 2008/02/10 · arxiv updated 2009/12/01
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.