Holonomic gradient descent and its application to the Fisher-Bingham integral

Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara, Tomonari Sei, Nobuki Takayama, Akimichi Takemura

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

We give a new algorithm to find local maxima and minima of a holonomic function and apply it for the Fisher-Bingham integral on the sphere Sn, which is used in the directional statistics. The method utilizes the theory and algorithms of holonomic systems.

Original languageEnglish
Pages (from-to)639-658
Number of pages20
JournalAdvances in Applied Mathematics
Volume47
Issue number3
DOIs
Publication statusPublished - 2011 Sep

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Gradient Descent
Directional Statistics
Statistics

Keywords

  • D-modules
  • Directional statistics
  • Fisher-Bingham distribution
  • Gradient descent
  • Gröbner basis
  • Holonomic function
  • Maximum likelihood

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Nakayama, H., Nishiyama, K., Noro, M., Ohara, K., Sei, T., Takayama, N., & Takemura, A. (2011). Holonomic gradient descent and its application to the Fisher-Bingham integral. Advances in Applied Mathematics, 47(3), 639-658. https://doi.org/10.1016/j.aam.2011.03.001

Holonomic gradient descent and its application to the Fisher-Bingham integral. / Nakayama, Hiromasa; Nishiyama, Kenta; Noro, Masayuki; Ohara, Katsuyoshi; Sei, Tomonari; Takayama, Nobuki; Takemura, Akimichi.

In: Advances in Applied Mathematics, Vol. 47, No. 3, 09.2011, p. 639-658.

Research output: Contribution to journalArticle

Nakayama, H, Nishiyama, K, Noro, M, Ohara, K, Sei, T, Takayama, N & Takemura, A 2011, 'Holonomic gradient descent and its application to the Fisher-Bingham integral', Advances in Applied Mathematics, vol. 47, no. 3, pp. 639-658. https://doi.org/10.1016/j.aam.2011.03.001
Nakayama, Hiromasa ; Nishiyama, Kenta ; Noro, Masayuki ; Ohara, Katsuyoshi ; Sei, Tomonari ; Takayama, Nobuki ; Takemura, Akimichi. / Holonomic gradient descent and its application to the Fisher-Bingham integral. In: Advances in Applied Mathematics. 2011 ; Vol. 47, No. 3. pp. 639-658.
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