On a Convergence Property of a Geometrical Algorithm for Statistical Manifolds

Shotaro Akaho, Hideitsu Hino, Noboru Murata

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish
Title of host publicationNeural Information Processing - 26th International Conference, ICONIP 2019, Proceedings
EditorsTom Gedeon, Kok Wai Wong, Minho Lee
PublisherSpringer
Pages262-272
Number of pages11
ISBN (Print)9783030368012
DOIs
Publication statusPublished - 2019
Event26th International Conference on Neural Information Processing, ICONIP 2019 - Sydney, Australia
Duration: 2019 Dec 122019 Dec 15

Publication series

NameCommunications in Computer and Information Science
Volume1143 CCIS
ISSN (Print)1865-0929
ISSN (Electronic)1865-0937

Conference

Conference26th International Conference on Neural Information Processing, ICONIP 2019
CountryAustralia
CitySydney
Period19/12/1219/12/15

Keywords

  • Dimension reduction
  • Information geometry
  • Mixture model
  • Pythagorean theorem

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

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  • Cite this

    Akaho, S., Hino, H., & Murata, N. (2019). On a Convergence Property of a Geometrical Algorithm for Statistical Manifolds. In T. Gedeon, K. W. Wong, & M. Lee (Eds.), Neural Information Processing - 26th International Conference, ICONIP 2019, Proceedings (pp. 262-272). (Communications in Computer and Information Science; Vol. 1143 CCIS). Springer. https://doi.org/10.1007/978-3-030-36802-9_29