Annotation of OpenXM/src/hgm/doc/ref-hgm.html, Revision 1.8
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5: <title>References for HGM</title> <!-- Use UTF-8 文字 code-->
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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>
1.8 ! takayama 15: <li> J.Hayakawa, A.Takemura,
! 16: Estimation of exponential-polynomial distribution by holonomic gradient descent
! 17: <a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
! 18:
! 19: <li> C.Siriteanu, A.Takemura, S.Kuriki,
! 20: MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
! 21: <a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
! 22:
1.4 takayama 23: <li> T.Koyama,
1.1 takayama 24: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
25: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
26:
27: <li> T.Hibi, K.Nishiyama, N.Takayama,
28: Pfaffian Systems of A-Hypergeometric Equations I,
29: Bases of Twisted Cohomology Groups,
30: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
31: (major revision v2 of arxiv:1212.6103)
32:
33: <li> <img src="./wakaba01.png" alt="Intro">
34: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
35: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
36:
37: <li> <img src="./wakaba01.png" alt="Intro">
38: Introduction to the Holonomic Gradient Method (movie), 2013.
39: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
40:
1.2 takayama 41:
1.1 takayama 42: <li> T.Sei, A.Kume,
1.2 takayama 43: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1 takayama 44: Statistics and Computing, 2013,
45: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
46:
1.4 takayama 47: <li> T.Koyama, A.Takemura,
1.2 takayama 48: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
49: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
50:
1.1 takayama 51: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
52: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
53: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
54: to appear in Journal of Pure and Applied Algebra
55:
56: <li>
57: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
58: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
59: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
60: Computational Statistics (2013)
61: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
62:
63: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
64: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
65: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
66: Journal of Multivariate Analysis, 117, (2013) 296-312,
67: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
68:
69: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
70: Properties and applications of Fisher distribution on the rotation group,
71: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
72: Journal of Multivariate Analysis, 116 (2013), 440--455,
73: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
74:
75: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
76: Funkcialaj Ekvacioj 56 (2013), 51--61.
77: <!-- <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a> -->
78: <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a>
79:
80: <li>
81: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
82: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
83: Holonomic Gradient Descent and its Application to Fisher-Bingham Integral,
84: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> -->
85: Advances in Applied Mathematics 47 (2011), 639--658,
86: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
87: </ol>
88:
1.2 takayama 89: <h2> Three Steps of HGM </h2>
90: <ol>
91: <li> Find a holonomic system satisfied by the normalizing constant.
92: We may use computational or theoretical methods to find it.
93: Groebner basis and related methods are used.
94: <li> Find an initial value vector for the holonomic system.
95: This is equivalent to evaluating the normalizing constant and its derivatives
96: at a point.
97: This step is usually performed by a series expansion.
98: <li> Solve the holonomic system numerically. We use several methods
99: in numerical analysis such as the Runge-Kutta method of solving
100: ordinary differential equations and efficient solvers of systems of linear
101: equations.
102: </ol>
103:
1.1 takayama 104: <h2> Software Packages for HGM</h2>
1.6 takayama 105: Most software packages are experimental and temporary documents are found in
106: "asir-contrib manual" (auto-autogenerated part), or
107: "Experimental Functions in Asir", or "miscellaneous and other documents"
108: of the
109: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7 takayama 110: OpenXM documents</a>
1.8 ! takayama 111: or in <a href="./"> this folder</a>.
1.6 takayama 112: The nightly snapshot of the asir-contrib can be found in the Asir-Contrib page below,
113: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8 ! takayama 114: cvsweb page</a>.
1.1 takayama 115: <ol>
1.2 takayama 116: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/hgm/"> hgm package for R </a> for the step 3.
1.1 takayama 117: <li> yang (for Pfaffian systems) , nk_restriction (for D-module integrations),
1.5 takayama 118: tk_jack (for Jack polynomials), ko_fb_pfaffian (Pfaffian system for the Fisher-Bingham system)
119: are for the steps 1 or 2 and in the
1.8 ! takayama 120: <a href="http://www.math.kobe-u.ac.jp/Asir"> asir-contrib</a>.
1.5 takayama 121: <li> nk_fb_gen_c is a package to generate a C program to perform
1.7 takayama 122: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.5 takayama 123: It is in the
1.8 ! takayama 124: <a href="http://www.math.kobe-u.ac.jp/Asir"> asir-contrib</a>.
1.1 takayama 125: </ol>
126:
127: <h2> Programs to try examples of our papers </h2>
128: <ol>
129: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
130: </ol>
131:
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