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

doi:10.1016/j.aam.2011.03.001

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 journal › Article › peer-review

39 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 language	English
Pages (from-to)	639-658
Number of pages	20
Journal	Advances in Applied Mathematics
Volume	47
Issue number	3
DOIs	https://doi.org/10.1016/j.aam.2011.03.001
Publication status	Published - 2011 Sept
Externally published	Yes

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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10.1016/j.aam.2011.03.001

Cite this

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title = "Holonomic gradient descent and its application to the Fisher-Bingham integral",

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.",

keywords = "D-modules, Directional statistics, Fisher-Bingham distribution, Gradient descent, Gr{\"o}bner basis, Holonomic function, Maximum likelihood",

author = "Hiromasa Nakayama and Kenta Nishiyama and Masayuki Noro and Katsuyoshi Ohara and Tomonari Sei and Nobuki Takayama and Akimichi Takemura",

note = "Funding Information: E-mail address: takayama@math.kobe-u.ac.jp (N. Takayama). 1 Author belongs to the JST crest Hibi project. 2 Supported by Kakenhi 22540179. 3 Supported by Kakenhi 19204008.",

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T1 - Holonomic gradient descent and its application to the Fisher-Bingham integral

AU - Nakayama, Hiromasa

AU - Nishiyama, Kenta

AU - Noro, Masayuki

AU - Ohara, Katsuyoshi

AU - Sei, Tomonari

AU - Takayama, Nobuki

AU - Takemura, Akimichi

N1 - Funding Information: E-mail address: takayama@math.kobe-u.ac.jp (N. Takayama). 1 Author belongs to the JST crest Hibi project. 2 Supported by Kakenhi 22540179. 3 Supported by Kakenhi 19204008.

PY - 2011/9

Y1 - 2011/9

N2 - 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.

AB - 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.

KW - D-modules

KW - Directional statistics

KW - Fisher-Bingham distribution

KW - Gradient descent

KW - Gröbner basis

KW - Holonomic function

KW - Maximum likelihood

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JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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