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Path Connectedness on a Space of Probability Density Functions

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Geometric Science of Information (GSI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9389))

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Abstract

We introduce a class of paths or one-parameter models connecting arbitrary two probability density functions (pdf’s). The class is derived by employing the Kolmogorov-Nagumo average between the two pdf’s. There is a variety of such path connectedness on the space of pdf’s since the Kolmogorov-Nagumo average is applicable for any convex and strictly increasing function. The information geometric insight is provided for understanding probabilistic properties for statistical methods associated with the path connectedness. The one-parameter model is extended to a multidimensional model, on which the statistical inference is characterized by sufficient statistics.

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Acknowledgments

Authors were supported by Japan Science and Technology Agency (JST), Core Research for Evolutionary Science and Technology (CREST), and express sincere gratitude to the reviewers for their helpful comments and suggestions for improving the original manuscript.

Author information

Authors and Affiliations

  1. Institute of Statistical Mathematics, Tachikawa, Tokyo, 190-8562, Japan

    Shinto Eguchi

  2. University of Fukui, Fukui, 910-8507, Japan

    Osamu Komori

Authors
  1. Shinto Eguchi
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  2. Osamu Komori
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Correspondence to Osamu Komori .

Editor information

Editors and Affiliations

  1. Bâtiment Alan Turing, CS35003, École Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land\& Air Systems, Limours, France

    Frédéric Barbaresco

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Eguchi, S., Komori, O. (2015). Path Connectedness on a Space of Probability Density Functions. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_66

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  • DOI: https://doi.org/10.1007/978-3-319-25040-3_66

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25039-7

  • Online ISBN: 978-3-319-25040-3

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