On kernel estimators of density ratio

Chen, Sy Mien; Hsu, Yu Sheng; Liaw, J. T.

doi:10.1080/02331880802496399

Cited by 21 publications

(13 citation statements)

References 9 publications

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“…where κn(·; σ) is a symmetric n-dimensional density estimation kernel with bandwidth parameter σ, and | · | denotes the cardinality of a set. The Radon-Nikodym derivative dU/dV in R n can be consistently estimated, under appropriate conditions, by the ratio of the Parzen estimates of the Radon-Nikodym derivatives f n U = dU/dμ and f n V = dV/dμ respectively, where μ denotes the Lebesgue measure [2]. Then, the estimator of the χ 2 -divergence becomeŝ…”

Section: Stratified Representationmentioning

confidence: 99%

Estimation of symmetric chi-square divergence for point processes

Park

Seth

Rao

et al. 2011

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper addresses the estimation of symmetric χ 2 -divergence between two point processes. We propose a novel approach by, first, mapping the space of spike trains in an appropriate functional space, and then, estimating the divergence in this functional space using a least square regression approach. We compare the proposed approach with other available methods on simulated data, and discuss its pros and cons.

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Section: Stratified Representationmentioning

confidence: 99%

Estimation of symmetric chi-square divergence for point processes

Park

Seth

Rao

et al. 2011

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…By construction, this estimator keeps the nonnegativity. Second, we are carefully examining the asymptotic negligibility of the remainder term of the stochastic expansion, in the spirit of Chen et al (2009) (see Igarashi and Kakizawa (2018a)). The basic tools are the Rosenthal and Bennett inequalities of the absolute moment and tail probability of the sum of zero-mean independent random variables (and their conditional variants).…”

Section: Overview Of the Papermentioning

confidence: 99%

Multiplicative bias correction for asymmetric kernel density estimators revisited

Igarashi

Kakizawa

2020

Computational Statistics & Data Analysis

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This paper revisits multiplicative bias correction for some asymmetric kernel density estimators (KDEs) when the data is supported on [0, ∞) d or [0, 1] d. The original method was introduced by Jones et al. (1995) for the standard KDE with symmetric kernel. After Hirukawa (2010) for beta KDE, there have been renewed interests for applications to the asymmetric KDEs. We stress that the variance manipulation must be performed by looking at four terms from the law of total variance/covariance, in which only one term is negligible, while other three terms contribute to the variance formula. It turns out that, even for recently developed asymmetric KDEs, the achievement of the reduced bias is available, at the expense of the constant-factor inflation of the variance. Interestingly, the same factor appears in other bias correction methods.

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“…Following this idea, various methods of importance estimation have been developed, for example, based on density estimation of p ′( x ) after uniformization of p ( x ), logistic regression for discriminating data from p ( x ) and p ′( x ), moment matching between p ′( x ) and p ( x ) w ( x ), integral equations between p ′( x ) and p ( x ) w ( x ), density matching between p ′( x ) and p ( x ) w ( x ) under the Kullback–Leibler divergence, least‐squares importance fitting of w ( x ) to p ′( x )/ p ( x ), and importance fitting of w ( x ) to p ′( x )/ p ( x ) under the Bregman divergence …”

Section: Adaptation Techniques For Covariate Shiftmentioning

confidence: 99%

Learning under nonstationarity: covariate shift and class‐balance change

Sugiyama

Yamada

Plessis

2013

WIREs Computational Stats

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One of the fundamental assumptions behind many supervised machine-learning algorithms is that training and test data follow the same probability distribution. However, this important assumption is often violated in practice, for example, because of an unavoidable sample selection bias or nonstationarity of the environment. Owing to violation of the assumption, standard machine-learning methods suffer a significant estimation bias. In this article, we consider two scenarios of such distribution change-the covariate shift where input distributions differ and class-balance change where class-prior probabilities vary in classification-and review semi-supervised adaptation techniques based on importance weighting. FIGURE 1 | Covariate shift. Input distributions change but the conditional distribution of outputs given inputs does not change. (a) Input densities and importance, (b) Learning target function, training samples, and test samples.466

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On kernel estimators of density ratio

Cited by 21 publications

References 9 publications

Estimation of symmetric chi-square divergence for point processes

Estimation of symmetric chi-square divergence for point processes

Multiplicative bias correction for asymmetric kernel density estimators revisited

Learning under nonstationarity: covariate shift and class‐balance change

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