Approximate inference of the bandwidth in multivariate kernel density estimation

Maurizio Filippone*, Guido Sanguinetti

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

Kernel density estimation is a popular and widely used non-parametric method for data-driven density estimation. Its appeal lies in its simplicity and ease of implementation, as well as its strong asymptotic results regarding its convergence to the true data distribution. However, a major difficulty is the setting of the bandwidth, particularly in high dimensions and with limited amount of data. An approximate Bayesian method is proposed, based on the ExpectationPropagation algorithm with a likelihood obtained from a leave-one-out cross validation approach. The proposed method yields an iterative procedure to approximate the posterior distribution of the inverse bandwidth. The approximate posterior can be used to estimate the model evidence for selecting the structure of the bandwidth and approach online learning. Extensive experimental validation shows that the proposed method is competitive in terms of performance with state-of-the-art plug-in methods.

Original languageEnglish (US)
Pages (from-to)3104-3122
Number of pages19
JournalComputational Statistics and Data Analysis
Volume55
Issue number12
DOIs
StatePublished - Dec 1 2011

Keywords

  • Bayesian inference
  • Expectation propagation
  • Kernel density estimation
  • Multivariate analysis

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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