Annotation of OpenXM/src/hgm/doc/ref-hgm.html, Revision 1.3
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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>
1.3 ! takayama 15: <li> T.Koyama, A.Takemura,
1.1 takayama 16: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
17: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
18:
19: <li> T.Hibi, K.Nishiyama, N.Takayama,
20: Pfaffian Systems of A-Hypergeometric Equations I,
21: Bases of Twisted Cohomology Groups,
22: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
23: (major revision v2 of arxiv:1212.6103)
24:
25: <li> <img src="./wakaba01.png" alt="Intro">
26: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
27: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
28:
29: <li> <img src="./wakaba01.png" alt="Intro">
30: Introduction to the Holonomic Gradient Method (movie), 2013.
31: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
32:
1.2 takayama 33:
1.1 takayama 34: <li> T.Sei, A.Kume,
1.2 takayama 35: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1 takayama 36: Statistics and Computing, 2013,
37: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
38:
1.2 takayama 39: <li> T.Koyama,
40: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
41: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
42:
1.1 takayama 43: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
44: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
45: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
46: to appear in Journal of Pure and Applied Algebra
47:
48: <li>
49: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
50: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
51: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
52: Computational Statistics (2013)
53: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
54:
55: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
56: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
57: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
58: Journal of Multivariate Analysis, 117, (2013) 296-312,
59: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
60:
61: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
62: Properties and applications of Fisher distribution on the rotation group,
63: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
64: Journal of Multivariate Analysis, 116 (2013), 440--455,
65: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
66:
67: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
68: Funkcialaj Ekvacioj 56 (2013), 51--61.
69: <!-- <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a> -->
70: <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a>
71:
72: <li>
73: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
74: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
75: Holonomic Gradient Descent and its Application to Fisher-Bingham Integral,
76: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> -->
77: Advances in Applied Mathematics 47 (2011), 639--658,
78: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
79: </ol>
80:
1.2 takayama 81: <h2> Three Steps of HGM </h2>
82: <ol>
83: <li> Find a holonomic system satisfied by the normalizing constant.
84: We may use computational or theoretical methods to find it.
85: Groebner basis and related methods are used.
86: <li> Find an initial value vector for the holonomic system.
87: This is equivalent to evaluating the normalizing constant and its derivatives
88: at a point.
89: This step is usually performed by a series expansion.
90: <li> Solve the holonomic system numerically. We use several methods
91: in numerical analysis such as the Runge-Kutta method of solving
92: ordinary differential equations and efficient solvers of systems of linear
93: equations.
94: </ol>
95:
1.1 takayama 96: <h2> Software Packages for HGM</h2>
97: <ol>
1.2 takayama 98: <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 99: <li> yang (for Pfaffian systems) , nk_restriction (for D-module integrations),
1.2 takayama 100: tk_jack (for Jack polynomials) are for the steps 1 or 2 and in the
1.1 takayama 101: <a href="http://www.math.kobe-u.ac.jp/Asir"> asir-contrib </a>
102: </ol>
103:
104: <h2> Programs to try examples of our papers </h2>
105: <ol>
106: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
107: </ol>
108:
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