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1.13 takayama 6: <!-- Do not edit this file. Edit it under OpenXM/src/hgm/doc -->
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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:
1.17 ! takayama 34: <li> C.Siriteanu, A.Takemura, C.Koutschan, S.Kuriki, D.St.P.Richards, H.Sin,
! 35: Exact ZF Analysis and Computer-Algebra-Aided Evaluation
! 36: in Rank-1 LoS Rician Fading,
! 37: <a href="http://arxiv.org/abs/1507.07056"> arxiv:1507.07056 </a>
! 38:
1.13 takayama 39: <li> K.Ohara, N.Takayama,
40: Pfaffian Systems of A-Hypergeometric Systems II ---
41: Holonomic Gradient Method,
42: <a href="http://arxiv.org/abs/1505.02947"> arxiv:1505.02947 </a>
43:
44: <li> T.Koyama,
45: The Annihilating Ideal of the Fisher Integral,
46: <a href="http://arxiv.org/abs/1503.05261"> arxiv:1503.05261 </a>
47:
48: <li> T.Koyama, A.Takemura,
49: Holonomic gradient method for distribution function of a weighted sum
50: of noncentral chi-square random variables,
51: <a href="http://arxiv.org/abs/1503.00378"> arxiv:1503.00378 </a>
52:
53: <li> Y.Goto,
54: Contiguity relations of Lauricella's F_D revisited,
55: <a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a>
1.12 takayama 56:
1.15 takayama 57: <li>
58: T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama,
59: Software Packages for Holonomic Gradient Method,
60: Mathematial Software --- ICMS 2014,
61: 4th International Conference, Proceedings.
62: Edited by Hoon Hong and Chee Yap,
63: Springer lecture notes in computer science 8592,
64: 706--712.
65: <a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_105">
66: DOI
67: </a>
68:
1.11 takayama 69: <li>N.Marumo, T.Oaku, A.Takemura,
70: Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
71: <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
72:
1.8 takayama 73: <li> J.Hayakawa, A.Takemura,
74: Estimation of exponential-polynomial distribution by holonomic gradient descent
75: <a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
76:
77: <li> C.Siriteanu, A.Takemura, S.Kuriki,
78: MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
79: <a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
80:
1.4 takayama 81: <li> T.Koyama,
1.1 takayama 82: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
83: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
84:
85: <li> T.Hibi, K.Nishiyama, N.Takayama,
86: Pfaffian Systems of A-Hypergeometric Equations I,
87: Bases of Twisted Cohomology Groups,
88: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
89: (major revision v2 of arxiv:1212.6103)
90:
91: <li> <img src="./wakaba01.png" alt="Intro">
92: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
93: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
94:
95: <li> <img src="./wakaba01.png" alt="Intro">
96: Introduction to the Holonomic Gradient Method (movie), 2013.
97: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
98:
1.2 takayama 99:
1.1 takayama 100: <li> T.Sei, A.Kume,
1.2 takayama 101: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1 takayama 102: Statistics and Computing, 2013,
103: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
104:
1.4 takayama 105: <li> T.Koyama, A.Takemura,
1.2 takayama 106: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
107: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
108:
1.1 takayama 109: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
110: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
111: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
1.11 takayama 112: Journal of Pure and Applied Algebra (online),
113: <a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
1.1 takayama 114:
115: <li>
116: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
117: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
118: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
119: Computational Statistics (2013)
120: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
121:
122: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
123: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
124: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
125: Journal of Multivariate Analysis, 117, (2013) 296-312,
126: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
127:
128: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
129: Properties and applications of Fisher distribution on the rotation group,
130: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
131: Journal of Multivariate Analysis, 116 (2013), 440--455,
132: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
133:
134: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
135: Funkcialaj Ekvacioj 56 (2013), 51--61.
1.11 takayama 136: <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
137: <!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
1.1 takayama 138:
139: <li>
140: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
141: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
142: Holonomic Gradient Descent and its Application to Fisher-Bingham Integral,
143: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> -->
144: Advances in Applied Mathematics 47 (2011), 639--658,
145: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
1.13 takayama 146:
1.1 takayama 147: </ol>
148:
1.13 takayama 149: Early papers related to HGM. <br>
150: <ol>
151: <li>
152: H.Dwinwoodie, L.Matusevich, E. Mosteig,
153: Transform methods for the hypergeometric distribution,
154: Statistics and Computing 14 (2004), 287--297.
155: </ol>
156:
157:
158:
1.2 takayama 159: <h2> Three Steps of HGM </h2>
160: <ol>
1.10 takayama 161: <li> Finding a holonomic system satisfied by the normalizing constant.
1.2 takayama 162: We may use computational or theoretical methods to find it.
163: Groebner basis and related methods are used.
1.10 takayama 164: <li> Finding an initial value vector for the holonomic system.
1.2 takayama 165: This is equivalent to evaluating the normalizing constant and its derivatives
166: at a point.
167: This step is usually performed by a series expansion.
1.10 takayama 168: <li> Solving the holonomic system numerically. We use several methods
1.2 takayama 169: in numerical analysis such as the Runge-Kutta method of solving
170: ordinary differential equations and efficient solvers of systems of linear
171: equations.
172: </ol>
173:
1.1 takayama 174: <h2> Software Packages for HGM</h2>
1.14 takayama 175:
1.15 takayama 176: <ul>
177: <li>
1.16 takayama 178: CRAN package <a href="https://cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).
1.14 takayama 179:
1.15 takayama 180: <li>
1.14 takayama 181: Some software packages are experimental and temporary documents are found in
1.6 takayama 182: "asir-contrib manual" (auto-autogenerated part), or
183: "Experimental Functions in Asir", or "miscellaneous and other documents"
184: of the
185: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7 takayama 186: OpenXM documents</a>
1.8 takayama 187: or in <a href="./"> this folder</a>.
1.10 takayama 188: The nightly snapshot of the asir-contrib can be found in the asir page below,
1.6 takayama 189: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8 takayama 190: cvsweb page</a>.
1.1 takayama 191: <ol>
1.9 takayama 192: <li> Command line interfaces are in the folder OpenXM/src/hgm
193: in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
194: OpenXM distribution page </a>.
1.14 takayama 195: <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 196: To install this package in R, type in
197: <pre>
198: R CMD install hgm_*.tar.gz
199: </pre>
1.10 takayama 200: <li> The following packages are
201: for the computer algebra system
202: <a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
203: They are in the asir-contrib collection.
204: <ul>
205: <li> yang.rr (for Pfaffian systems) ,
206: nk_restriction.rr (for D-module integrations),
207: tk_jack.rr (for Jack polynomials),
208: ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
209: are for the steps 1 or 2.
210: <li> nk_fb_gen_c.rr is a package to generate a C program to perform
1.7 takayama 211: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.10 takayama 212: <li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
213: </ul>
1.1 takayama 214: </ol>
215:
1.15 takayama 216: </ul>
217:
1.1 takayama 218: <h2> Programs to try examples of our papers </h2>
219: <ol>
220: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
221: </ol>
222:
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