Direct Density Ratio Estimation for Large-scale Covariate Shift Adaptation

Tsuboi, Yuta; Kashima, Hisashi; Hido, Shohei; Bickel, Steffen; Sugiyama, Masashi

doi:10.2197/ipsjjip.17.138

Cited by 105 publications

(66 citation statements)

References 9 publications

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“…Tsuboi et al (2008) have pointed out a similar relation for the M-estimator based on the Kullback-Leibler divergence. Now we give an interpretation of (15) through an analogous optimization example in the Euclidean space.…”

Section: Kernel Mean Matching (Kmm)mentioning

confidence: 57%

Statistical analysis of kernel-based least-squares density-ratio estimation

2011

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The ratio of two probability densities can be used for solving various machine learning tasks such as covariate shift adaptation (importance sampling), outlier detection (likelihood-ratio test), feature selection (mutual information), and conditional probability estimation. Several methods of directly estimating the density ratio have recently been developed, e.g., moment matching estimation, maximum-likelihood density-ratio estimation, and least-squares density-ratio fitting. In this paper, we propose a kernelized variant of the least-squares method for density-ratio estimation, which is called kernel unconstrained leastsquares importance fitting (KuLSIF). We investigate its fundamental statistical properties including a non-parametric convergence rate, an analytic-form solution, and a leave-oneout cross-validation score. We further study its relation to other kernel-based density-ratio estimators. In experiments, we numerically compare various kernel-based density-ratio estimation methods, and show that KuLSIF compares favorably with other approaches.

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Section: Kernel Mean Matching (Kmm)mentioning

confidence: 57%

Statistical analysis of kernel-based least-squares density-ratio estimation

2011

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“…Covariate shift is a situation in supervised learning where the training and test input distributions are different while the conditional distribution of output remains unchanged [2]. In many real-world applications such as robot control [3], bioinformatics [4], spam filtering [5], natural language processing [6], brain-computer interfacing [7], and speaker identification [8], covariate shift adaptation has been shown to be useful. Covariate shift is also naturally induced in selective sampling or active learning scenarios and adaptation improves the generalization performance [9]- [12].…”

Section: Introductionmentioning

confidence: 99%

Direct Importance Estimation with Gaussian Mixture Models

Yamada

Sugiyama

2009

IEICE Trans. Inf. & Syst.

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SUMMARYThe ratio of two probability densities is called the importance and its estimation has gathered a great deal of attention these days since the importance can be used for various data processing purposes. In this paper, we propose a new importance estimation method using Gaussian mixture models (GMMs). Our method is an extention of the Kullback-Leibler importance estimation procedure (KLIEP), an importance estimation method using linear or kernel models. An advantage of GMMs is that covariance matrices can also be learned through an expectation-maximization procedure, so the proposed method-which we call the Gaussian mixture KLIEP (GM-KLIEP)-is expected to work well when the true importance function has high correlation. Through experiments, we show the validity of the proposed approach.

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“…Similarly, applying the direct density-ration estimation method based on the log-loss called the Kullback-Leibler Importance Estimation Procedure (KLIEP) [28], [29], [37], [38], [43], [44], [48], we can obtain a log-loss variant of the proposed method. A valiant of the KLIEP method explored in the papers [43], [44] uses a log-linear model (a.k.a. a maximum entropy model [16]) for density ratio estimation:…”

Section: Discussionmentioning

confidence: 99%

“…Other methods of direct density ratio estimation [28], [29], [37], [38], [43], [44], [48] employs the KullbackLeibler divergence [22] as the loss function, instead of the squared-loss. It is possible to use these methods for conditional density estimation in the same way as the proposed method, but it is computationally rather inefficient [17], [18].…”

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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Direct Density Ratio Estimation for Large-scale Covariate Shift Adaptation

Cited by 105 publications

References 9 publications

Statistical analysis of kernel-based least-squares density-ratio estimation

Statistical analysis of kernel-based least-squares density-ratio estimation

Direct Importance Estimation with Gaussian Mixture Models

Least-Squares Conditional Density Estimation

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