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Approximate inference of the bandwidth in multivariate kernel density estimation

Author

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  • Filippone, Maurizio
  • Sanguinetti, Guido

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 Expectation-Propagation 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.

Suggested Citation

  • Filippone, Maurizio & Sanguinetti, Guido, 2011. "Approximate inference of the bandwidth in multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3104-3122, December.
  • Handle: RePEc:eee:csdana:v:55:y:2011:i:12:p:3104-3122
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    References listed on IDEAS

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    Cited by:

    1. Y. Ziane & S. Adjabi & N. Zougab, 2015. "Adaptive Bayesian bandwidth selection in asymmetric kernel density estimation for nonnegative heavy-tailed data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(8), pages 1645-1658, August.
    2. Zougab, Nabil & Adjabi, Smail & Kokonendji, Célestin C., 2014. "Bayesian estimation of adaptive bandwidth matrices in multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 28-38.
    3. repec:spr:compst:v:33:y:2018:i:1:d:10.1007_s00180-017-0712-8 is not listed on IDEAS
    4. repec:eee:csdana:v:119:y:2018:i:c:p:139-154 is not listed on IDEAS

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