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Coordinate-Wise Transformation and Stein-Type Densities

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Geometric Science of Information (GSI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10589))

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Abstract

A Stein-type density function is defined as a stationary point of the free-energy functional over a fiber that consists of probability densities obtained by coordinate-wise transformations of a given density. It is shown that under some conditions there exists a unique Stein-type density in each fiber. An application to rating is discussed.

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Acknowledgements

The author is grateful to three anonymous referees for their constructive comments. This work was supported by JSPS KAKENHI Grant Numbers JP26108003 and JP17K00044.

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Authors and Affiliations

  1. The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

    Tomonari Sei

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  1. Tomonari Sei
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Correspondence to Tomonari Sei .

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Editors and Affiliations

  1. Ecole Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land and Air Systems, Limours, France

    Frédéric Barbaresco

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Sei, T. (2017). Coordinate-Wise Transformation and Stein-Type Densities. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science(), vol 10589. Springer, Cham. https://doi.org/10.1007/978-3-319-68445-1_77

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  • DOI: https://doi.org/10.1007/978-3-319-68445-1_77

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68444-4

  • Online ISBN: 978-3-319-68445-1

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