hgm-package: HGM

In hgm: Holonomic Gradient Method and Gradient Descent

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

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.

Note

This package includes a small subset of the Gnu scientific library codes (http://www.gnu.org/software/gsl/). Then, it might cause a conflict with the package gsl.

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, doi: 10.1016/j.aam.2011.03.001

• (dojo) Edited by T.Hibi, Groebner Bases: Statistics and Software Systems, Springer, 2013, doi: 10.1007/978-4-431-54574-3

• http://www.openxm.org

See Also

hgm.ncBingham, hgm.ncorthant, hgm.ncso3, hgm.pwishart, hgm.Rhgm hgm.p2wishart,

Examples

## Not run: 
example(hgm.ncBingham)
example(hgm.ncorthant)
example(hgm.ncso3)
example(hgm.pwishart)
example(hgm.Rhgm)
example(hgm.p2wishart)

## End(Not run)

hgm documentation built on Feb. 16, 2023, 7:44 p.m.