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

29 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 1

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics

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  • 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