Least-Squares Conditional Density Estimation

Masashi SUGIYAMA  Ichiro TAKEUCHI  Taiji SUZUKI  Takafumi KANAMORI  Hirotaka HACHIYA  Daisuke OKANOHARA  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E93-D   No.3   pp.583-594
Publication Date: 2010/03/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E93.D.583
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Pattern Recognition
Keyword: 
conditional density estimation,  multimodality,  heteroscedastic noise,  direct density ratio estimation,  transition estimation,  

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Summary: 
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.