hgm (version 1.10)

hgm-package: HGM

Description

The holonomic gradient method (HGM, hgm) gives a way to evaluate normalizing constants of unnormalized probability distributions by utilizing holonomic systems of differential or difference equations. The holonomic gradient descent (HGD, hgd) gives a method to find maximal likelihood estimates by utilizing the HGM.

Details

ll{ Package: hgm Type: Package License: GPL-2 LazyLoad: yes } The HGM and HGD are proposed in the paper below. This method based on the fact that a broad class of normalizing constants of unnormalized probability distributions belongs to the class of holonomic functions, which are solutions of holonomic systems of linear partial differential equations.

References

• [N3OST2] Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara, Tomonari Sei, Nobuki Takayama, Akimichi Takemura, Holonomic Gradient Descent and its Application to Fisher-Bingham Integral, Advances in Applied Mathematics 47 (2011), 639--658,http://dx.doi.org/10.1016/j.aam.2011.03.001
• [dojo] Edited by T.Hibi, Groebner Bases: Statistics and Software Systems, Springer, 2013,http://dx.doi.org/10.1007/978-4-431-54574-3
• http://www.openxm.org

See Also

hgm.ncBingham, hgm.ncorthant, hgm.ncso3, hgm.pwishart, hgm.Rhgm

Examples

example(hgm.ncBingham)
example(hgm.ncorthant)
example(hgm.ncso3)
example(hgm.pwishart)
example(hgm.Rhgm)