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%% $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm-package.Rd,v 1.7 2014/03/25 02:25:26 takayama Exp $ |
%% $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm-package.Rd,v 1.10 2014/03/31 07:23:09 takayama Exp $ |
\name{hgm-package} |
\name{hgm-package} |
\alias{hgm-package} |
\alias{hgm-package} |
\alias{HGM} |
\alias{HGM} |
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|
HGM |
HGM |
} |
} |
\description{ |
\description{ |
The holonomic gradient method (HGM, hgm) gives a way to evaluate normalization |
The holonomic gradient method (HGM, hgm) gives a way to evaluate normalizing |
constants of unnormalized probability distributions by utilizing holonomic |
constants of unnormalized probability distributions by utilizing holonomic |
systems of differential equations. |
systems of differential or difference equations. |
The holonomic gradient descent (HGD, hgd) gives a method |
The holonomic gradient descent (HGD, hgd) gives a method |
to find maximal likelihood estimates by utilizing the HGM. |
to find maximal likelihood estimates by utilizing the HGM. |
} |
} |
Line 22 License: \tab GPL-2\cr |
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Line 22 License: \tab GPL-2\cr |
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LazyLoad: \tab yes\cr |
LazyLoad: \tab yes\cr |
} |
} |
The HGM and HGD are proposed in the paper below. |
The HGM and HGD are proposed in the paper below. |
This method based on the fact that a broad class of normalization constants |
This method based on the fact that a broad class of normalizing constants |
of unnormalized probability distributions belongs to the class of |
of unnormalized probability distributions belongs to the class of |
holonomic functions, which are solutions of holonomic systems of linear |
holonomic functions, which are solutions of holonomic systems of linear |
partial differential equations. |
partial differential equations. |
Line 38 partial differential equations. |
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Line 38 partial differential equations. |
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} |
} |
\references{ |
\references{ |
\itemize{ |
\itemize{ |
\item Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara, |
\item [N3OST2] Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara, |
Tomonari Sei, Nobuki Takayama, Akimichi Takemura, |
Tomonari Sei, Nobuki Takayama, Akimichi Takemura, |
Holonomic Gradient Descent and its Application to Fisher-Bingham Integral, |
Holonomic Gradient Descent and its Application to Fisher-Bingham Integral, |
Advances in Applied Mathematics 47 (2011), 639--658, |
Advances in Applied Mathematics 47 (2011), 639--658, |
\url{http://dx.doi.org/10.1016/j.aam.2011.03.001} |
\url{http://dx.doi.org/10.1016/j.aam.2011.03.001} |
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\item [dojo] Edited by T.Hibi, Groebner Bases: Statistics and Software Systems, Springer, 2013, |
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\url{http://dx.doi.org/10.1007/978-4-431-54574-3} |
\item \url{http://www.openxm.org} |
\item \url{http://www.openxm.org} |
} |
} |
} |
} |
Line 53 Advances in Applied Mathematics 47 (2011), 639--658, |
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Line 54 Advances in Applied Mathematics 47 (2011), 639--658, |
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\keyword{ HGM } |
\keyword{ HGM } |
\keyword{ HGD } |
\keyword{ HGD } |
\seealso{ |
\seealso{ |
\code{\link{hgm.ncBingham}} |
\code{\link{hgm.mleFBByOptim}}, |
\code{\link{hgm.ncorthant}} |
\code{\link{hgm.ncBingham}}, |
\code{\link{hgm.ncso3}} |
\code{\link{hgm.ncorthant}}, |
\code{\link{hgm.pwishart}} |
\code{\link{hgm.ncso3}}, |
|
\code{\link{hgm.pwishart}}, |
\code{\link{hgm.Rhgm}} |
\code{\link{hgm.Rhgm}} |
} |
} |
\examples{ |
\examples{ |