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Neural Computation

February 2009, Vol. 21, No. 2, Pages 533-559
(doi: 10.1162/neco.2008.10-07-628)
© 2008 Massachusetts Institute of Technology
Nonparametric Conditional Density Estimation Using Piecewise-Linear Solution Path of Kernel Quantile Regression
Article PDF (1.09 MB)
Abstract

The goal of regression analysis is to describe the stochastic relationship between an input vector x and a scalar output y. This can be achieved by estimating the entire conditional density p(yx). In this letter, we present a new approach for nonparametric conditional density estimation. We develop a piecewise-linear path-following method for kernel-based quantile regression. It enables us to estimate the cumulative distribution function of p(yx) in piecewise-linear form for all x in the input domain. Theoretical analyses and experimental results are presented to show the effectiveness of the approach.