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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>
1.12 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,
1.13 takayama 17: <a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637 </a>
18:
19: <li> T.Koyama,
20: Holonomic gradient method for the probability content of a simplex
21: region
22: with a multivariate normal distribution,
23: <a href="http://arxiv.org/abs/1512.06564"> arxiv:1512.06564 </a>
24:
25:
26: <li> N.Takayama, S.Kuriki, A.Takemura,
27: A-Hpergeometric Distributions and Newton Polytopes,
28: <a href="http://arxiv.org/abs/1510.02269"> arxiv:1510.02269 </a>
29:
30: <li> G.Weyenberg, R.Yoshida, D.Howe,
31: Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace,
32: <a href="http://arxiv.org/abs/1506.00142"> arxiv:1506.00142 </a>
33:
34: <li> K.Ohara, N.Takayama,
35: Pfaffian Systems of A-Hypergeometric Systems II ---
36: Holonomic Gradient Method,
37: <a href="http://arxiv.org/abs/1505.02947"> arxiv:1505.02947 </a>
38:
39: <li> T.Koyama,
40: The Annihilating Ideal of the Fisher Integral,
41: <a href="http://arxiv.org/abs/1503.05261"> arxiv:1503.05261 </a>
42:
43: <li> T.Koyama, A.Takemura,
44: Holonomic gradient method for distribution function of a weighted sum
45: of noncentral chi-square random variables,
46: <a href="http://arxiv.org/abs/1503.00378"> arxiv:1503.00378 </a>
47:
48: <li> Y.Goto,
49: Contiguity relations of Lauricella's F_D revisited,
50: <a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a>
1.12 takayama 51:
1.15 takayama 52: <li>
53: T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama,
54: Software Packages for Holonomic Gradient Method,
55: Mathematial Software --- ICMS 2014,
56: 4th International Conference, Proceedings.
57: Edited by Hoon Hong and Chee Yap,
58: Springer lecture notes in computer science 8592,
59: 706--712.
60: <a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_105">
61: DOI
62: </a>
63:
1.11 takayama 64: <li>N.Marumo, T.Oaku, A.Takemura,
65: Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
66: <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
67:
1.8 takayama 68: <li> J.Hayakawa, A.Takemura,
69: Estimation of exponential-polynomial distribution by holonomic gradient descent
70: <a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
71:
72: <li> C.Siriteanu, A.Takemura, S.Kuriki,
73: MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
74: <a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
75:
1.4 takayama 76: <li> T.Koyama,
1.1 takayama 77: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
78: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
79:
80: <li> T.Hibi, K.Nishiyama, N.Takayama,
81: Pfaffian Systems of A-Hypergeometric Equations I,
82: Bases of Twisted Cohomology Groups,
83: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
84: (major revision v2 of arxiv:1212.6103)
85:
86: <li> <img src="./wakaba01.png" alt="Intro">
87: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
88: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
89:
90: <li> <img src="./wakaba01.png" alt="Intro">
91: Introduction to the Holonomic Gradient Method (movie), 2013.
92: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
93:
1.2 takayama 94:
1.1 takayama 95: <li> T.Sei, A.Kume,
1.2 takayama 96: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1 takayama 97: Statistics and Computing, 2013,
98: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
99:
1.4 takayama 100: <li> T.Koyama, A.Takemura,
1.2 takayama 101: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
102: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
103:
1.1 takayama 104: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
105: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
106: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
1.11 takayama 107: Journal of Pure and Applied Algebra (online),
108: <a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
1.1 takayama 109:
110: <li>
111: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
112: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
113: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
114: Computational Statistics (2013)
115: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
116:
117: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
118: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
119: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
120: Journal of Multivariate Analysis, 117, (2013) 296-312,
121: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
122:
123: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
124: Properties and applications of Fisher distribution on the rotation group,
125: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
126: Journal of Multivariate Analysis, 116 (2013), 440--455,
127: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
128:
129: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
130: Funkcialaj Ekvacioj 56 (2013), 51--61.
1.11 takayama 131: <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
132: <!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
1.1 takayama 133:
134: <li>
135: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
136: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
137: Holonomic Gradient Descent and its Application to Fisher-Bingham Integral,
138: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> -->
139: Advances in Applied Mathematics 47 (2011), 639--658,
140: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
1.13 takayama 141:
1.1 takayama 142: </ol>
143:
1.13 takayama 144: Early papers related to HGM. <br>
145: <ol>
146: <li>
147: H.Dwinwoodie, L.Matusevich, E. Mosteig,
148: Transform methods for the hypergeometric distribution,
149: Statistics and Computing 14 (2004), 287--297.
150: </ol>
151:
152:
153:
1.2 takayama 154: <h2> Three Steps of HGM </h2>
155: <ol>
1.10 takayama 156: <li> Finding a holonomic system satisfied by the normalizing constant.
1.2 takayama 157: We may use computational or theoretical methods to find it.
158: Groebner basis and related methods are used.
1.10 takayama 159: <li> Finding an initial value vector for the holonomic system.
1.2 takayama 160: This is equivalent to evaluating the normalizing constant and its derivatives
161: at a point.
162: This step is usually performed by a series expansion.
1.10 takayama 163: <li> Solving the holonomic system numerically. We use several methods
1.2 takayama 164: in numerical analysis such as the Runge-Kutta method of solving
165: ordinary differential equations and efficient solvers of systems of linear
166: equations.
167: </ol>
168:
1.1 takayama 169: <h2> Software Packages for HGM</h2>
1.14 takayama 170:
1.15 takayama 171: <ul>
172: <li>
1.16 ! takayama 173: CRAN package <a href="https://cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).
1.14 takayama 174:
1.15 takayama 175: <li>
1.14 takayama 176: Some software packages are experimental and temporary documents are found in
1.6 takayama 177: "asir-contrib manual" (auto-autogenerated part), or
178: "Experimental Functions in Asir", or "miscellaneous and other documents"
179: of the
180: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7 takayama 181: OpenXM documents</a>
1.8 takayama 182: or in <a href="./"> this folder</a>.
1.10 takayama 183: The nightly snapshot of the asir-contrib can be found in the asir page below,
1.6 takayama 184: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8 takayama 185: cvsweb page</a>.
1.1 takayama 186: <ol>
1.9 takayama 187: <li> Command line interfaces are in the folder OpenXM/src/hgm
188: in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
189: OpenXM distribution page </a>.
1.14 takayama 190: <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.
1.11 takayama 191: To install this package in R, type in
192: <pre>
193: R CMD install hgm_*.tar.gz
194: </pre>
1.10 takayama 195: <li> The following packages are
196: for the computer algebra system
197: <a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
198: They are in the asir-contrib collection.
199: <ul>
200: <li> yang.rr (for Pfaffian systems) ,
201: nk_restriction.rr (for D-module integrations),
202: tk_jack.rr (for Jack polynomials),
203: ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
204: are for the steps 1 or 2.
205: <li> nk_fb_gen_c.rr is a package to generate a C program to perform
1.7 takayama 206: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.10 takayama 207: <li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
208: </ul>
1.1 takayama 209: </ol>
210:
1.15 takayama 211: </ul>
212:
1.1 takayama 213: <h2> Programs to try examples of our papers </h2>
214: <ol>
215: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
216: </ol>
217:
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