<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//JA" "http://www.w3.org/TR/REC-html40/loose.dtd">
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<meta name="viewport" content="width=device-width,initial-scale=1.0,minimum-scale=1.0">
<!-- for mobile friendly -->
<title>References for HGM</title> <!-- Use UTF-8 文字 code-->
<!-- Do not edit this file. Edit it under OpenXM/src/hgm/doc -->
</head>
<body>
<h1> References for the Holonomic Gradient Method (HGM) and
the Holonomic Gradient Descent Method (HGD) </h1>
<h2> Papers and Tutorials</h2>
<ol>
<li> Nobuki Takayama, Takaharu Yaguchi, Yi Zhang,
Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics,
<a href="https://arxiv.org/abs/2111.10947"> arxiv:2111.10947 </a>
<li> Shuhei Mano, Nobuki Takayama,
Algebraic algorithm for direct sampling from toric models,
<a href="https://arxiv.org/abs/2110.14992"> arxiv:2110.14992 </a>
<li> M.Adamer, A.Lorincz, A.L.Sattelberger, B.Sturmfels, Algebraic Analysis of Rotation Data
<a href="https://arxiv.org/abs/1912.00396"> arxiv: 1912.00396 </a>
<li>
Anna-Laura Sattelberger, Bernd Sturmfels,
D-Modules and Holonomic Functions
<a href="https://arxiv.org/abs/1910.01395"> arxiv:1910.01395 </a>
<li>
N.Takayama, L.Jiu, S.Kuriki, Y.Zhang,
Computations of the Expected Euler Characteristic for the Largest Eigenvalue of a Real Wishart Matrix,
<!--
<a href="https://arxiv.org/abs/1903.10099"> arxiv:1903.10099 </a> -->
<a href="https://doi.org/10.1016/j.jmva.2020.104642"> jmva </a>
<li> M.Harkonen, T.Sei, Y.Hirose,
Holonomic extended least angle regression,
<a href="https://arxiv.org/abs/1809.08190"> arxiv:1809.08190 </a>
<li> S.Mano,
Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics,
<a href="https://www.springer.com/jp/book/9784431558866">
JSS Research Series in Statistics</a>, 2018.
<li> A.Kume, T.Sei,
On the exact maximum likelihood inference of Fisher–Bingham distributions using an adjusted holonomic gradient method,
<a href="https://doi.org/10.1007/s11222-017-9765-3"> doi </a> (2018)
<li> Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama, Nobuki Takayama,
Holonomic Gradient Method for Two Way Contingency Tables,
<a href="https://arxiv.org/abs/1803.04170"> arxiv:1803.04170 </a>
<li> F.H.Danufane, K.Ohara, N.Takayama, C.Siriteanu,
Holonomic Gradient Method-Based CDF Evaluation for the Largest Eigenvalue of a Complex Noncentral Wishart Matrix
(Title of the version 1: Holonomic Gradient Method for the Distribution Function of the Largest Root of Complex Non-central Wishart Matrices),
<a href="https://arxiv.org/abs/1707.02564"> arxiv:1707.02564 </a>
<li> T.Koyama,
An integral formula for the powered sum of the independent, identically and normally distributed random variables,
<a href="https://arxiv.org/abs/1706.03989"> arxiv:1706.03989 </a>
<li> H.Hashiguchi, N.Takayama, A.Takemura,
Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability
by Holonomic Gradient Method,
<a href="https://arxiv.org/abs/1610.09187"> arxiv:1610.09187 </a>
<li> R.Vidunas, A.Takemura,
Differential relations for the largest root distribution
of complex non-central Wishart matrices,
<a href="http://arxiv.org/abs/1609.01799"> arxiv:1609.01799 </a>
<li> S.Mano,
The A-hypergeometric System Associated with the Rational Normal Curve and
Exchangeable Structures,
<a href="http://doi.org/10.1214/17-EJS1361"> doi </a>,
<a href="http://arxiv.org/abs/1607.03569"> arxiv:1607.03569 </a>
<li> M.Noro,
System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions,
<a href="http://dl.acm.org/citation.cfm?doid=2930889.2930905"> ACM DL </a>
<li> Y.Goto, K.Matsumoto,
Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications,
<a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637 </a>
<li> T.Koyama,
Holonomic gradient method for the probability content of a simplex
region
with a multivariate normal distribution,
<a href="http://arxiv.org/abs/1512.06564"> arxiv:1512.06564 </a>
<li> N.Takayama, Holonomic Gradient Method (in Japanese, survey),
<a href="http://www.math.kobe-u.ac.jp/HOME/taka/2015/hgm-dic.pdf">
hgm-dic.pdf </a>
<li> N.Takayama, S.Kuriki, A.Takemura,
A-Hpergeometric Distributions and Newton Polytopes,
<a href="http://arxiv.org/abs/1510.02269"> arxiv:1510.02269 </a>
<li> G.Weyenberg, R.Yoshida, D.Howe,
Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace,
<a href="http://arxiv.org/abs/1506.00142"> arxiv:1506.00142 </a>
<li> C.Siriteanu, A.Takemura, C.Koutschan, S.Kuriki, D.St.P.Richards, H.Sin,
Exact ZF Analysis and Computer-Algebra-Aided Evaluation
in Rank-1 LoS Rician Fading,
<a href="http://arxiv.org/abs/1507.07056"> arxiv:1507.07056 </a>
<li> K.Ohara, N.Takayama,
Pfaffian Systems of A-Hypergeometric Systems II ---
Holonomic Gradient Method,
<a href="http://arxiv.org/abs/1505.02947"> arxiv:1505.02947 </a>
<li> T.Koyama,
The Annihilating Ideal of the Fisher Integral,
<a href="http://arxiv.org/abs/1503.05261"> arxiv:1503.05261 </a>
<li> T.Koyama, A.Takemura,
Holonomic gradient method for distribution function of a weighted sum
of noncentral chi-square random variables,
<a href="http://arxiv.org/abs/1503.00378"> arxiv:1503.00378 </a>
<li> Y.Goto,
Contiguity relations of Lauricella's F_D revisited,
<a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a>
<li>
T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama,
Software Packages for Holonomic Gradient Method,
Mathematial Software --- ICMS 2014,
4th International Conference, Proceedings.
Edited by Hoon Hong and Chee Yap,
Springer lecture notes in computer science 8592,
706--712.
<a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_105">
DOI
</a>
<li>N.Marumo, T.Oaku, A.Takemura,
Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
<a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
<li> J.Hayakawa, A.Takemura,
Estimation of exponential-polynomial distribution by holonomic gradient descent
<a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
<li> C.Siriteanu, A.Takemura, S.Kuriki,
MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
<a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
<li> T.Koyama,
Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
<a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
<li> T.Hibi, K.Nishiyama, N.Takayama,
Pfaffian Systems of A-Hypergeometric Equations I,
Bases of Twisted Cohomology Groups,
<a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
(major revision v2 of arxiv:1212.6103).
Accepted version is at
<a href="http://dx.doi.org/10.1016/j.aim.2016.10.021"> DOI </a>
<li> <img src="./wakaba01.png" alt="Intro">
<a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
<li> <img src="./wakaba01.png" alt="Intro">
Introduction to the Holonomic Gradient Method (movie), 2013.
<a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
<li> T.Sei, A.Kume,
Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
Statistics and Computing, 2013,
<a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
<li> T.Koyama, A.Takemura,
Calculation of Orthant Probabilities by the Holonomic Gradient Method,
<a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
<li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
Holonomic Rank of the Fisher-Bingham System of Differential Equations,
<!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
Journal of Pure and Applied Algebra (online),
<a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
<li>
T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
<!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
Computational Statistics (2013)
<a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
<li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
<!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
Journal of Multivariate Analysis, 117, (2013) 296-312,
<a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
<li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
Properties and applications of Fisher distribution on the rotation group,
<!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
Journal of Multivariate Analysis, 116 (2013), 440--455,
<a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
<li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
Funkcialaj Ekvacioj 56 (2013), 51--61.
<a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
<!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
<li>
Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
Holonomic Gradient Descent and its Application to Fisher-Bingham Integral,
<!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> -->
Advances in Applied Mathematics 47 (2011), 639--658,
<a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
</ol>
Early papers related to HGM. <br>
<ol>
<li>
H.Dwinwoodie, L.Matusevich, E. Mosteig,
Transform methods for the hypergeometric distribution,
Statistics and Computing 14 (2004), 287--297.
</ol>
<h2> Three Steps of HGM </h2>
<ol>
<li> Finding a holonomic system satisfied by the normalizing constant.
We may use computational or theoretical methods to find it.
Groebner basis and related methods are used.
<li> Finding an initial value vector for the holonomic system.
This is equivalent to evaluating the normalizing constant and its derivatives
at a point.
This step is usually performed by a series expansion.
<li> Solving the holonomic system numerically. We use several methods
in numerical analysis such as the Runge-Kutta method of solving
ordinary differential equations and efficient solvers of systems of linear
equations.
</ol>
<h2> Software Packages for HGM</h2>
<ul>
<li>
CRAN package <a href="https://cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).
<li>
Some software packages are experimental and temporary documents are found in
"asir-contrib manual" (auto-autogenerated part), or
"Experimental Functions in Asir", or "miscellaneous and other documents"
of the
<a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
OpenXM documents</a>
or in <a href="./"> this folder</a>.
The nightly snapshot of the asir-contrib can be found in the asir page below,
or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
cvsweb page</a>.
<ol>
<li> Command line interfaces are in the folder OpenXM/src/hgm
in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
OpenXM distribution page </a>.
<li> Experimental version of <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/hgm/"> hgm package for R </a> (hgm_*tar.gz, hgm-manual.pdf) for the step 3.
To install this package in R, type in
<pre>
R CMD install hgm_*.tar.gz
</pre>
<li> The following packages are
for the computer algebra system
<a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
They are in the asir-contrib collection.
<ul>
<li> yang.rr (for Pfaffian systems) ,
nk_restriction.rr (for D-module integrations),
tk_jack.rr (for Jack polynomials),
ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
are for the steps 1 or 2.
<li> nk_fb_gen_c.rr is a package to generate a C program to perform
maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
<li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
</ul>
</ol>
</ul>
<h2> Programs to try examples of our papers </h2>
<ol>
<li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
</ol>
<pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.34 2022/08/21 21:47:08 takayama Exp $ </pre>
</body>
</html>
![[BACK]](/icons/cvsweb/back.gif){kind=icon}
Return to ref-hgm.html CVS log ![[TXT]](/icons/cvsweb/text.gif){kind=icon}
![[DIR]](/icons/cvsweb/dir.gif){kind=icon}
Up to [local] / OpenXM / src / hgm / doc