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TitleHolonomic gradient descent and its application to the Fisher–Bingham integral
Author(s) Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara, Tomonari Sei, Nobuki Takayama, Akimichi Takemura
TypeArticle in Journal
AbstractWe 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 S n , which is used in the directional statistics. The method utilizes the theory and algorithms of holonomic systems.
KeywordsHolonomic function, Maximum likelihood, Gradient descent, Directional statistics, D-modules, Gröbner basis, Fisher–Bingham distribution
ISSN0196-8858
URL http://www.sciencedirect.com/science/article/pii/S019688581100008X
LanguageEnglish
JournalAdvances in Applied Mathematics
Volume47
Number3
Pages639 - 658
Year2011
Edition0
Translation No
Refereed No
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