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

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 S n , which is used in the directional statistics. The method utilizes the theory and algorithms of holonomic systems.

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Bibliographic Details
Published in:Advances in applied mathematics 2011-09, Vol.47 (3), p.639-658
Main Authors: Nakayama, Hiromasa, Nishiyama, Kenta, Noro, Masayuki, Ohara, Katsuyoshi, Sei, Tomonari, Takayama, Nobuki, Takemura, Akimichi
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Commutative rings and algebras
D-modules
Descent
Directional statistics
Exact sciences and technology
Fisher–Bingham distribution
General mathematics
General, history and biography
Gradient descent
Gröbner basis
Holonomic function
Integrals
Mathematical analysis
Mathematics
Maxima
Maximum likelihood
Minima
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Statistics
Tin
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Description
Summary: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 S n , which is used in the directional statistics. The method utilizes the theory and algorithms of holonomic systems.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2011.03.001