# Conditional Density Estimation via Least-Squares Density Ratio Estimation

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Masashi Sugiyama,
Ichiro Takeuchi,
Taiji Suzuki,
Takafumi Kanamori,
Hirotaka Hachiya,
Daisuke Okanohara
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Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:781-788, 2010.

#### Abstract

Estimating the conditional mean of an input-output 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 that is suitable for multi-dimensional continuous variables. The basic idea of the proposed method is to express the conditional density in terms of the density ratio 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.

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