Nonparametric Conditional Density Estimation Using Piecewise-Linear Solution Path of Kernel Quantile Regression

Ichiro Takeuchi, Kaname Nomura, Takafumi Kanamori

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(y ∣ x). 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(y ∣ x) 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.