Annotation of OpenXM/src/hgm/doc/ref-hgm.html, Revision 1.12
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10: <h1> References for the Holonomic Gradient Method (HGM) and
11: the Holonomic Gradient Descent Method (HGD) </h1>
12:
13: <h2> Papers and Tutorials</h2>
14: <ol>
1.12 ! takayama 15: <li> Y.Goto, K.Matsumoto,
! 16: Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications,
! 17: <a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637
! 18:
1.11 takayama 19: <li>N.Marumo, T.Oaku, A.Takemura,
20: Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
21: <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
22:
1.8 takayama 23: <li> J.Hayakawa, A.Takemura,
24: Estimation of exponential-polynomial distribution by holonomic gradient descent
25: <a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
26:
27: <li> C.Siriteanu, A.Takemura, S.Kuriki,
28: MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
29: <a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
30:
1.4 takayama 31: <li> T.Koyama,
1.1 takayama 32: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
33: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
34:
35: <li> T.Hibi, K.Nishiyama, N.Takayama,
36: Pfaffian Systems of A-Hypergeometric Equations I,
37: Bases of Twisted Cohomology Groups,
38: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
39: (major revision v2 of arxiv:1212.6103)
40:
41: <li> <img src="./wakaba01.png" alt="Intro">
42: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
43: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
44:
45: <li> <img src="./wakaba01.png" alt="Intro">
46: Introduction to the Holonomic Gradient Method (movie), 2013.
47: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
48:
1.2 takayama 49:
1.1 takayama 50: <li> T.Sei, A.Kume,
1.2 takayama 51: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1 takayama 52: Statistics and Computing, 2013,
53: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
54:
1.4 takayama 55: <li> T.Koyama, A.Takemura,
1.2 takayama 56: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
57: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
58:
1.1 takayama 59: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
60: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
61: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
1.11 takayama 62: Journal of Pure and Applied Algebra (online),
63: <a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
1.1 takayama 64:
65: <li>
66: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
67: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
68: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
69: Computational Statistics (2013)
70: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
71:
72: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
73: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
74: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
75: Journal of Multivariate Analysis, 117, (2013) 296-312,
76: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
77:
78: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
79: Properties and applications of Fisher distribution on the rotation group,
80: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
81: Journal of Multivariate Analysis, 116 (2013), 440--455,
82: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
83:
84: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
85: Funkcialaj Ekvacioj 56 (2013), 51--61.
1.11 takayama 86: <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
87: <!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
1.1 takayama 88:
89: <li>
90: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
91: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
92: Holonomic Gradient Descent and its Application to Fisher-Bingham Integral,
93: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> -->
94: Advances in Applied Mathematics 47 (2011), 639--658,
95: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
96: </ol>
97:
1.2 takayama 98: <h2> Three Steps of HGM </h2>
99: <ol>
1.10 takayama 100: <li> Finding a holonomic system satisfied by the normalizing constant.
1.2 takayama 101: We may use computational or theoretical methods to find it.
102: Groebner basis and related methods are used.
1.10 takayama 103: <li> Finding an initial value vector for the holonomic system.
1.2 takayama 104: This is equivalent to evaluating the normalizing constant and its derivatives
105: at a point.
106: This step is usually performed by a series expansion.
1.10 takayama 107: <li> Solving the holonomic system numerically. We use several methods
1.2 takayama 108: in numerical analysis such as the Runge-Kutta method of solving
109: ordinary differential equations and efficient solvers of systems of linear
110: equations.
111: </ol>
112:
1.1 takayama 113: <h2> Software Packages for HGM</h2>
1.6 takayama 114: Most software packages are experimental and temporary documents are found in
115: "asir-contrib manual" (auto-autogenerated part), or
116: "Experimental Functions in Asir", or "miscellaneous and other documents"
117: of the
118: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7 takayama 119: OpenXM documents</a>
1.8 takayama 120: or in <a href="./"> this folder</a>.
1.10 takayama 121: The nightly snapshot of the asir-contrib can be found in the asir page below,
1.6 takayama 122: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8 takayama 123: cvsweb page</a>.
1.1 takayama 124: <ol>
1.9 takayama 125: <li> Command line interfaces are in the folder OpenXM/src/hgm
126: in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
127: OpenXM distribution page </a>.
1.11 takayama 128: <li> <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.
129: To install this package in R, type in
130: <pre>
131: R CMD install hgm_*.tar.gz
132: </pre>
1.10 takayama 133: <li> The following packages are
134: for the computer algebra system
135: <a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
136: They are in the asir-contrib collection.
137: <ul>
138: <li> yang.rr (for Pfaffian systems) ,
139: nk_restriction.rr (for D-module integrations),
140: tk_jack.rr (for Jack polynomials),
141: ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
142: are for the steps 1 or 2.
143: <li> nk_fb_gen_c.rr is a package to generate a C program to perform
1.7 takayama 144: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.10 takayama 145: <li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
146: </ul>
1.1 takayama 147: </ol>
148:
149: <h2> Programs to try examples of our papers </h2>
150: <ol>
151: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
152: </ol>
153:
1.12 ! takayama 154: <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.11 2014/05/20 02:12:18 takayama Exp $ </pre>
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