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On a Convergence Property of a Geometrical Algorithm for Statistical Manifolds

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Neural Information Processing (ICONIP 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1143))

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Abstract

In this paper, we examine a geometrical projection algorithm for statistical inference. The algorithm is based on Pythagorean relation and it is derivative-free as well as representation-free that is useful in nonparametric cases. We derive a bound of learning rate to guarantee local convergence. In special cases of m-mixture and e-mixture estimation problems, we calculate specific forms of the bound that can be used easily in practice.

Supported by JSPS KAKENHI Grant Number 17H01793, 19K12111.

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Notes

  1. 1.

    Details of the proof will appear in the full version of the paper [3].

References

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Author information

Authors and Affiliations

  1. National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki, 305-8568, Japan

    Shotaro Akaho

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

    Hideitsu Hino

  3. Waseda University, Shinjuku, Tokyo, 169-0072, Japan

    Noboru Murata

  4. RIKEN Center for Advanced Intelligence Project, Chuo, Tokyo, 103-0027, Japan

    Shotaro Akaho, Hideitsu Hino & Noboru Murata

Authors
  1. Shotaro Akaho
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  2. Hideitsu Hino
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  3. Noboru Murata
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Corresponding author

Correspondence to Shotaro Akaho .

Editor information

Editors and Affiliations

  1. Australian National University, Canberra, ACT, Australia

    Tom Gedeon

  2. Murdoch University, Murdoch, WA, Australia

    Kok Wai Wong

  3. Kyungpook National University, Daegu, Korea (Republic of)

    Minho Lee

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Akaho, S., Hino, H., Murata, N. (2019). On a Convergence Property of a Geometrical Algorithm for Statistical Manifolds. In: Gedeon, T., Wong, K., Lee, M. (eds) Neural Information Processing. ICONIP 2019. Communications in Computer and Information Science, vol 1143. Springer, Cham. https://doi.org/10.1007/978-3-030-36802-9_29

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  • DOI: https://doi.org/10.1007/978-3-030-36802-9_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-36801-2

  • Online ISBN: 978-3-030-36802-9

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