Approximate inference of the bandwidth in multivariate kernel density estimation
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.
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- Kamila Żychaluk & Prakash Patil, 2008. "A cross-validation method for data with ties in kernel density estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(1), pages 21-44, March.
- Zhang, Xibin & Brooks, Robert D. & King, Maxwell L., 2009.
"A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation,"
Journal of Econometrics,
Elsevier, vol. 153(1), pages 21-32, November.
- Xibin Zhang & Robert D. Brooks & Maxwell L. King, 2007. "A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation," Monash Econometrics and Business Statistics Working Papers 11/07, Monash University, Department of Econometrics and Business Statistics.
- Duong, Tarn & Cowling, Arianna & Koch, Inge & Wand, M.P., 2008. "Feature significance for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4225-4242, May.
- Tran, Thanh N. & Wehrens, Ron & Buydens, Lutgarde M.C., 2006. "KNN-kernel density-based clustering for high-dimensional multivariate data," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 513-525, November.
- Zhang, Xibin & King, Maxwell L. & Hyndman, Rob J., 2006. "A Bayesian approach to bandwidth selection for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3009-3031, July.
- Hazelton, Martin L. & Turlach, Berwin A., 2007. "Reweighted kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3057-3069, March.
- Jones, M.C. & Henderson, D.A., 2009. "Maximum likelihood kernel density estimation: On the potential of convolution sieves," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3726-3733, August.
- van der Laan Mark J. & Dudoit Sandrine & Keles Sunduz, 2004. "Asymptotic Optimality of Likelihood-Based Cross-Validation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-25, March.
- N. Friel & A. N. Pettitt, 2008. "Marginal likelihood estimation via power posteriors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 589-607.
- Jones, M. C., 1991. "On correcting for variance inflation in kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 11(1), pages 3-15, January.
- Cao, Ricardo & Cuevas, Antonio & Gonzalez Manteiga, Wensceslao, 1994. "A comparative study of several smoothing methods in density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 17(2), pages 153-176, February.
- Calderhead, Ben & Girolami, Mark, 2009. "Estimating Bayes factors via thermodynamic integration and population MCMC," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4028-4045, October.
- Tarn Duong & Martin L. Hazelton, 2005. "Cross-validation Bandwidth Matrices for Multivariate Kernel Density Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 485-506.
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