Annotation of OpenXM/src/hgm/doc/ref-hgm.html, Revision 1.11
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9:
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>
1.11 ! takayama 15: <li>N.Marumo, T.Oaku, A.Takemura,
! 16: Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
! 17: <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
! 18:
1.8 takayama 19: <li> J.Hayakawa, A.Takemura,
20: Estimation of exponential-polynomial distribution by holonomic gradient descent
21: <a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
22:
23: <li> C.Siriteanu, A.Takemura, S.Kuriki,
24: MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
25: <a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
26:
1.4 takayama 27: <li> T.Koyama,
1.1 takayama 28: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
29: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
30:
31: <li> T.Hibi, K.Nishiyama, N.Takayama,
32: Pfaffian Systems of A-Hypergeometric Equations I,
33: Bases of Twisted Cohomology Groups,
34: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
35: (major revision v2 of arxiv:1212.6103)
36:
37: <li> <img src="./wakaba01.png" alt="Intro">
38: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
39: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
40:
41: <li> <img src="./wakaba01.png" alt="Intro">
42: Introduction to the Holonomic Gradient Method (movie), 2013.
43: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
44:
1.2 takayama 45:
1.1 takayama 46: <li> T.Sei, A.Kume,
1.2 takayama 47: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1 takayama 48: Statistics and Computing, 2013,
49: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
50:
1.4 takayama 51: <li> T.Koyama, A.Takemura,
1.2 takayama 52: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
53: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
54:
1.1 takayama 55: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
56: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
57: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
1.11 ! takayama 58: Journal of Pure and Applied Algebra (online),
! 59: <a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
1.1 takayama 60:
61: <li>
62: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
63: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
64: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
65: Computational Statistics (2013)
66: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
67:
68: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
69: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
70: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
71: Journal of Multivariate Analysis, 117, (2013) 296-312,
72: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
73:
74: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
75: Properties and applications of Fisher distribution on the rotation group,
76: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
77: Journal of Multivariate Analysis, 116 (2013), 440--455,
78: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
79:
80: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
81: Funkcialaj Ekvacioj 56 (2013), 51--61.
1.11 ! takayama 82: <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
! 83: <!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
1.1 takayama 84:
85: <li>
86: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
87: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
88: Holonomic Gradient Descent and its Application to Fisher-Bingham Integral,
89: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> -->
90: Advances in Applied Mathematics 47 (2011), 639--658,
91: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
92: </ol>
93:
1.2 takayama 94: <h2> Three Steps of HGM </h2>
95: <ol>
1.10 takayama 96: <li> Finding a holonomic system satisfied by the normalizing constant.
1.2 takayama 97: We may use computational or theoretical methods to find it.
98: Groebner basis and related methods are used.
1.10 takayama 99: <li> Finding an initial value vector for the holonomic system.
1.2 takayama 100: This is equivalent to evaluating the normalizing constant and its derivatives
101: at a point.
102: This step is usually performed by a series expansion.
1.10 takayama 103: <li> Solving the holonomic system numerically. We use several methods
1.2 takayama 104: in numerical analysis such as the Runge-Kutta method of solving
105: ordinary differential equations and efficient solvers of systems of linear
106: equations.
107: </ol>
108:
1.1 takayama 109: <h2> Software Packages for HGM</h2>
1.6 takayama 110: Most software packages are experimental and temporary documents are found in
111: "asir-contrib manual" (auto-autogenerated part), or
112: "Experimental Functions in Asir", or "miscellaneous and other documents"
113: of the
114: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7 takayama 115: OpenXM documents</a>
1.8 takayama 116: or in <a href="./"> this folder</a>.
1.10 takayama 117: The nightly snapshot of the asir-contrib can be found in the asir page below,
1.6 takayama 118: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8 takayama 119: cvsweb page</a>.
1.1 takayama 120: <ol>
1.9 takayama 121: <li> Command line interfaces are in the folder OpenXM/src/hgm
122: in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
123: OpenXM distribution page </a>.
1.11 ! takayama 124: <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.
! 125: To install this package in R, type in
! 126: <pre>
! 127: R CMD install hgm_*.tar.gz
! 128: </pre>
1.10 takayama 129: <li> The following packages are
130: for the computer algebra system
131: <a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
132: They are in the asir-contrib collection.
133: <ul>
134: <li> yang.rr (for Pfaffian systems) ,
135: nk_restriction.rr (for D-module integrations),
136: tk_jack.rr (for Jack polynomials),
137: ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
138: are for the steps 1 or 2.
139: <li> nk_fb_gen_c.rr is a package to generate a C program to perform
1.7 takayama 140: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.10 takayama 141: <li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
142: </ul>
1.1 takayama 143: </ol>
144:
145: <h2> Programs to try examples of our papers </h2>
146: <ol>
147: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
148: </ol>
149:
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