Generalized Dirichlet-process-means for f-separable distortion measures

Kobayashi, Masahiro; Watanabe, Kazuho

doi:10.1016/j.neucom.2020.03.123

Cited by 3 publications

(8 citation statements)

References 15 publications

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“…This section introduces the estimation method based on f -separable Bregman distortion measures [40]. We consider estimating the parameter θ ∈ Θ ⊆ R d of a statistical model p(x|θ) when given the data…”

Section: F -Separable Bregman Distortion Measuresmentioning

confidence: 99%

“…In this paper, we consider the M-estimation under fseparable distortion measures, which were proposed to extend linear distortion, such as the average distortion to nonlinear distortion, and for which the rate-distortion function was studied [39]. It was also used to solve the estimation problem with Bregman divergence as the base distortion measure, and a simple clustering or vector quantization algorithm was constructed [40]. In this paper, this class of objective functions is called the f -separable Bregman distortion measure.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Unbiased Estimating Equation and Latent Bias Under f-Separable Bregman Distortion Measures

Kobayashi,

Watanabe

2024

IEEE Trans. Inform. Theory

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We discuss unbiased estimating equations in a class of objective functions using a monotonically increasing function f and Bregman divergence. The choice of the function f gives desirable properties, such as robustness against outliers. To obtain unbiased estimating equations, analytically intractable integrals are generally required as bias correction terms. In this study, we clarify the combination of Bregman divergence, statistical model, and function f in which the bias correction term vanishes. Focusing on Mahalanobis and Itakura-Saito distances, we generalize fundamental existing results and characterize a class of distributions of positive reals with a scale parameter, including the gamma distribution as a special case. We also generalized these results to general model classes characterized by one-dimensional Bregman divergence. Furthermore, we discuss the possibility of latent bias minimization when the proportion of outliers is large, which is induced by the extinction of the bias correction term. We conducted numerical experiments to show that the latent bias can approach zero under heavy contamination of outliers or very small inliers.

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Section: F -Separable Bregman Distortion Measuresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Unbiased Estimating Equation and Latent Bias Under f-Separable Bregman Distortion Measures

Kobayashi,

Watanabe

2024

IEEE Trans. Inform. Theory

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“…Theorem 2: If the following condition holds against the combination of the function f and statistical model (12), the estimation equation holds without a bias correction term:…”

Section: B Is Distancementioning

confidence: 99%

“…In this paper, we consider the M-estimation under fseparable distortion measures, which were proposed to extend linear distortion such as the average distortion to non-linear distortion, and for which the rate-distortion function was studied [11]. It was also applied to the estimation problem with Bregman divergence as the base distortion measure and a simple clustering or vector quantization algorithm was constructed [12]. In this paper, we call this class of objective functions the f -separable Bregman distortion measure.…”

Section: Introductionmentioning

confidence: 99%

“…We compare the M-estimation under the f -separable IS distortion measure with the estimation methods minimizing β and γ divergences in terms of asymptotic efficiency. In this section, we introduce the estimation method based on f -separable Bregman distortion measures [12]. We consider estimating the parameter θ ∈ Θ ⊆ R d of a statistical model p(x|θ) when given the data…”

Section: Introductionmentioning

confidence: 99%

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Unbiased Estimation Equation under f-Separable Bregman Distortion Measures

Kobayashi

Watanabe

2021

2020 IEEE Information Theory Workshop (ITW)

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We discuss unbiased estimation equations in a class of objective function using a monotonically increasing function f and Bregman divergence. The choice of the function f gives desirable properties such as robustness against outliers. In order to obtain unbiased estimation equations, analytically intractable integrals are generally required as bias correction terms. In this study, we clarify the combination of Bregman divergence, statistical model, and function f in which the bias correction term vanishes. Focusing on Mahalanobis and Itakura-Saito distances, we provide a generalization of fundamental existing results and characterize a class of distributions of positive reals with a scale parameter, which includes the gamma distribution as a special case. We discuss the possibility of latent bias minimization when the proportion of outliers is large, which is induced by the extinction of the bias correction term.

show abstract

Unbiased Estimating Equation on Inverse Divergence and its Conditions

Kobayashi,

Watanabe

2024

2024 IEEE International Symposium on Information Theory (ISIT)

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Generalized Dirichlet-process-means for f-separable distortion measures

Cited by 3 publications

References 15 publications

Unbiased Estimating Equation and Latent Bias Under f-Separable Bregman Distortion Measures

Unbiased Estimating Equation and Latent Bias Under f-Separable Bregman Distortion Measures

Unbiased Estimation Equation under f-Separable Bregman Distortion Measures

Unbiased Estimating Equation on Inverse Divergence and its Conditions

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