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Change-point detection is the problem of finding points of time when a probability distribution of samples changed. There are various related problems, such as estimating the number of the change-points and estimating magnitude of the change. Though various statistical models have been assumed in the field of change-point detection, we particularly deal with i.p.i.d. (*independent-piecewise-identically-distributed*) sources. In this paper, we formulate the related problems in a general manner based on statistical decision theory. Then we derive optimal estimators for the problems under the Bayes risk principle. We also propose efficient algorithms for the change-point detection-related problems in the i.p.i.d. sources, while in general, the optimal estimations requires huge amount of calculation in Bayesian setting. Comparison of the proposed algorithm and previous methods are made through numerical examples.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E103-A No.12 pp.1393-1402

- Publication Date
- 2020/12/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2020TAP0009

- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)

- Category
- Machine Learning

Kairi SUZUKI

Waseda University

Akira KAMATSUKA

Waseda University

Toshiyasu MATSUSHIMA

Waseda University

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Kairi SUZUKI, Akira KAMATSUKA, Toshiyasu MATSUSHIMA, "A Bayesian Decision-Theoretic Change-Point Detection for i.p.i.d. Sources" in IEICE TRANSACTIONS on Fundamentals,
vol. E103-A, no. 12, pp. 1393-1402, December 2020, doi: 10.1587/transfun.2020TAP0009.

Abstract: Change-point detection is the problem of finding points of time when a probability distribution of samples changed. There are various related problems, such as estimating the number of the change-points and estimating magnitude of the change. Though various statistical models have been assumed in the field of change-point detection, we particularly deal with i.p.i.d. (*independent-piecewise-identically-distributed*) sources. In this paper, we formulate the related problems in a general manner based on statistical decision theory. Then we derive optimal estimators for the problems under the Bayes risk principle. We also propose efficient algorithms for the change-point detection-related problems in the i.p.i.d. sources, while in general, the optimal estimations requires huge amount of calculation in Bayesian setting. Comparison of the proposed algorithm and previous methods are made through numerical examples.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2020TAP0009/_p

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@ARTICLE{e103-a_12_1393,

author={Kairi SUZUKI, Akira KAMATSUKA, Toshiyasu MATSUSHIMA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={A Bayesian Decision-Theoretic Change-Point Detection for i.p.i.d. Sources},

year={2020},

volume={E103-A},

number={12},

pages={1393-1402},

abstract={Change-point detection is the problem of finding points of time when a probability distribution of samples changed. There are various related problems, such as estimating the number of the change-points and estimating magnitude of the change. Though various statistical models have been assumed in the field of change-point detection, we particularly deal with i.p.i.d. (*independent-piecewise-identically-distributed*) sources. In this paper, we formulate the related problems in a general manner based on statistical decision theory. Then we derive optimal estimators for the problems under the Bayes risk principle. We also propose efficient algorithms for the change-point detection-related problems in the i.p.i.d. sources, while in general, the optimal estimations requires huge amount of calculation in Bayesian setting. Comparison of the proposed algorithm and previous methods are made through numerical examples.},

keywords={},

doi={10.1587/transfun.2020TAP0009},

ISSN={1745-1337},

month={December},}

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TY - JOUR

TI - A Bayesian Decision-Theoretic Change-Point Detection for i.p.i.d. Sources

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1393

EP - 1402

AU - Kairi SUZUKI

AU - Akira KAMATSUKA

AU - Toshiyasu MATSUSHIMA

PY - 2020

DO - 10.1587/transfun.2020TAP0009

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E103-A

IS - 12

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - December 2020

AB - Change-point detection is the problem of finding points of time when a probability distribution of samples changed. There are various related problems, such as estimating the number of the change-points and estimating magnitude of the change. Though various statistical models have been assumed in the field of change-point detection, we particularly deal with i.p.i.d. (*independent-piecewise-identically-distributed*) sources. In this paper, we formulate the related problems in a general manner based on statistical decision theory. Then we derive optimal estimators for the problems under the Bayes risk principle. We also propose efficient algorithms for the change-point detection-related problems in the i.p.i.d. sources, while in general, the optimal estimations requires huge amount of calculation in Bayesian setting. Comparison of the proposed algorithm and previous methods are made through numerical examples.

ER -