Conditional Density Estimation via Least-Squares Density Ratio Estimation

Abstract

Estimating the conditional mean of an inputoutput relation is the goal of regression. However, regression analysis is not sufficiently informative if the conditional distribution has multi-modality, is highly asymmetric, or contains heteroscedastic noise. In such scenarios, estimating the conditional distribution itself would be more useful. In this paper, we propose a novel method of conditional density estimation. Our basic idea is to express the conditional density in terms of the ratio of unconditional densities, and the ratio is directly estimated without going through density estimation. Experiments using benchmark and robot transition datasets illustrate the usefulness of the proposed approach. 1