Semiparametric density estimation under a two-sample density ratio model

Cheng, Kuang Fu; Chu, Chih‐Peng

doi:10.3150/bj/1093265631

Cited by 60 publications

(44 citation statements)

References 13 publications

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“…However, this naive approach is not reliable in high-dimensional problems since division by an estimated quantity can magnify the estimation error of the dividend. To overcome this drawback, various approaches to directly estimating density-ratios without going through density estimation have been explored recently, including the moment matching approach (Gretton et al 2009), the probabilistic classification approach (Qin 1998;Cheng and Chu 2004), the density matching approach Tsuboi et al 2009;Yamada and Sugiyama 2009;Nguyen et al 2010;, and the density-ratio fitting approach ).…”

Section: Introductionmentioning

confidence: 99%

Density-ratio matching under the Bregman divergence: a unified framework of density-ratio estimation

2011

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Estimation of the ratio of probability densities has attracted a great deal of attention since it can be used for addressing various statistical paradigms. A naive approach to density-ratio approximation is to first estimate numerator and denominator densities separately and then take their ratio. However, this two-step approach does not perform well in practice, and methods for directly estimating density ratios without density estimation have been explored. In this paper, we first give a comprehensive review of existing density-ratio estimation methods and discuss their pros and cons. Then we propose a new framework of density-ratio estimation in which a density-ratio model is fitted to the true density-ratio under the Bregman divergence. Our new framework includes existing approaches as special cases, and is substantially more general. Finally, we develop a robust density-ratio estimation method under the power divergence, which is a novel instance in our framework.

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Section: Introductionmentioning

confidence: 99%

Density-ratio matching under the Bregman divergence: a unified framework of density-ratio estimation

2011

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“…2.3). The kernel mean matching method [14] and the logistic regression based method [3], [6], [30] also allow one to directly estimate a density ratio q(x)/q (x). However, the derivation of these methods heavily relies on the fact that the two density functions q(x) and q (x) share the same domain, which is not fulfilled in the current setting.…”

Section: Other Methods Of Density Ratio Estimationmentioning

confidence: 99%

Least-Squares Conditional Density Estimation

Sugiyama

Takeuchi

Suzuki

et al. 2010

IEICE Trans. Inf. & Syst.

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SUMMARYEstimating 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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“…We first give a comprehensive review of methods for estimating the density ratio, including the kernel density estimator 18) , kernel mean matching 4) , logistic regression 6), 19), 20) , the Kullback-Leibler importance estimation procedure 9), 10) , least-squares importance fitting 11) , and unconstrained least-squares importance fitting 11) . Note that "importance" refers to the density ratio, derived from importance sampling 21) .…”

Section: Introductionmentioning

confidence: 99%

A Density-ratio Framework for Statistical Data Processing

Sugiyama

Kanamori

Suzuki

et al. 2009

IPSJ Transactions on Computer Vision and Applications

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In statistical pattern recognition, it is important to avoid density estimation since density estimation is often more difficult than pattern recognition itself. Following this idea-known as Vapnik's principle, a statistical data processing framework that employs the ratio of two probability density functions has been developed recently and is gathering a lot of attention in the machine learning and data mining communities. The purpose of this paper is to introduce to the computer vision community recent advances in density ratio estimation methods and their usage in various statistical data processing tasks such as nonstationarity adaptation, outlier detection, feature selection, and independent component analysis.

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Semiparametric density estimation under a two-sample density ratio model

Cited by 60 publications

References 13 publications

Density-ratio matching under the Bregman divergence: a unified framework of density-ratio estimation

Density-ratio matching under the Bregman divergence: a unified framework of density-ratio estimation

Least-Squares Conditional Density Estimation

A Density-ratio Framework for Statistical Data Processing

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