On a Convergence Property of a Geometrical Algorithm for Statistical Manifolds

Shotaro Akaho; Hideitsu Hino; Noboru Murata

doi:10.1007/978-3-030-36802-9_29

On a Convergence Property of a Geometrical Algorithm for Statistical Manifolds

Shotaro Akaho^*, Hideitsu Hino, Noboru Murata

^*Corresponding author for this work

School of Advanced Science and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

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 language	English
Title of host publication	Neural Information Processing - 26th International Conference, ICONIP 2019, Proceedings
Editors	Tom Gedeon, Kok Wai Wong, Minho Lee
Publisher	Springer
Pages	262-272
Number of pages	11
ISBN (Print)	9783030368012
DOIs	https://doi.org/10.1007/978-3-030-36802-9_29
Publication status	Published - 2019
Event	26th International Conference on Neural Information Processing, ICONIP 2019 - Sydney, Australia Duration: 2019 Dec 12 → 2019 Dec 15

Publication series

Name	Communications in Computer and Information Science
Volume	1143 CCIS
ISSN (Print)	1865-0929
ISSN (Electronic)	1865-0937

Conference

Conference	26th International Conference on Neural Information Processing, ICONIP 2019
Country/Territory	Australia
City	Sydney
Period	19/12/12 → 19/12/15

Keywords

Dimension reduction
Information geometry
Mixture model
Pythagorean theorem

ASJC Scopus subject areas

Computer Science(all)
Mathematics(all)

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10.1007/978-3-030-36802-9_29

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

On a Convergence Property of a Geometrical Algorithm for Statistical Manifolds. / Akaho, Shotaro; Hino, Hideitsu; Murata, Noboru.
Neural Information Processing - 26th International Conference, ICONIP 2019, Proceedings. ed. / Tom Gedeon; Kok Wai Wong; Minho Lee. Springer, 2019. p. 262-272 (Communications in Computer and Information Science; Vol. 1143 CCIS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Akaho, S, Hino, H & Murata, N 2019, On a Convergence Property of a Geometrical Algorithm for Statistical Manifolds. in T Gedeon, KW Wong & M Lee (eds), Neural Information Processing - 26th International Conference, ICONIP 2019, Proceedings. Communications in Computer and Information Science, vol. 1143 CCIS, Springer, pp. 262-272, 26th International Conference on Neural Information Processing, ICONIP 2019, Sydney, Australia, 19/12/12. https://doi.org/10.1007/978-3-030-36802-9_29

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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.",

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On a Convergence Property of a Geometrical Algorithm for Statistical Manifolds

Abstract

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Keywords

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