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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>
1.24 ! takayama 15: <li> Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama, Nobuki Takayama,
! 16: Holonomic Gradient Method for Two Way Contingency Tables,
! 17: <a href="https://arxiv.org/abs/1803.04170"> arxiv:1803.04170
1.23 takayama 18: <li> F.H.Danufane, K.Ohara, N.Takayama,
19: Holonomic Gradient Method for the Distribution Function of the Largest Root of Complex Non-central Wishart Matrices,
20: <a href="https://arxiv.org/abs/1707.02564"> arxiv:1707.02564 </a>
21: <li> T.Koyama,
22: An integral formula for the powered sum of the independent, identically and normally distributed random variables,
23: <a href="https://arxiv.org/abs/1706.03989"> arxiv:1706.03989 </a>
1.21 takayama 24: <li> H.Hashiguchi, N.Takayama, A.Takemura,
25: Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability
26: by Holonomic Gradient Method,
27: <a href="https://arxiv.org/abs/1610.09187"> arxiv:1610.09187 </a>
28:
1.18 takayama 29: <li> R.Vidunas, A.Takemura,
30: Differential relations for the largest root distribution
31: of complex non-central Wishart matrices,
32: <a href="http://arxiv.org/abs/1609.01799"> arxiv:1609.01799 </a>
33:
1.20 takayama 34: <li> S.Mano,
35: The A-hypergeometric System Associated with the Rational Normal Curve and
36: Exchangeable Structures,
37: <a href="http://arxiv.org/abs/1607.03569"> arxiv:1607.03569 </a>
38:
1.19 takayama 39: <li> M.Noro,
40: System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions,
41: <a href="http://dl.acm.org/citation.cfm?doid=2930889.2930905"> ACM DL </a>
42:
1.12 takayama 43: <li> Y.Goto, K.Matsumoto,
44: Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications,
1.13 takayama 45: <a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637 </a>
46:
47: <li> T.Koyama,
48: Holonomic gradient method for the probability content of a simplex
49: region
50: with a multivariate normal distribution,
51: <a href="http://arxiv.org/abs/1512.06564"> arxiv:1512.06564 </a>
52:
53:
54: <li> N.Takayama, S.Kuriki, A.Takemura,
55: A-Hpergeometric Distributions and Newton Polytopes,
56: <a href="http://arxiv.org/abs/1510.02269"> arxiv:1510.02269 </a>
57:
58: <li> G.Weyenberg, R.Yoshida, D.Howe,
59: Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace,
60: <a href="http://arxiv.org/abs/1506.00142"> arxiv:1506.00142 </a>
61:
1.17 takayama 62: <li> C.Siriteanu, A.Takemura, C.Koutschan, S.Kuriki, D.St.P.Richards, H.Sin,
63: Exact ZF Analysis and Computer-Algebra-Aided Evaluation
64: in Rank-1 LoS Rician Fading,
65: <a href="http://arxiv.org/abs/1507.07056"> arxiv:1507.07056 </a>
66:
1.13 takayama 67: <li> K.Ohara, N.Takayama,
68: Pfaffian Systems of A-Hypergeometric Systems II ---
69: Holonomic Gradient Method,
70: <a href="http://arxiv.org/abs/1505.02947"> arxiv:1505.02947 </a>
71:
72: <li> T.Koyama,
73: The Annihilating Ideal of the Fisher Integral,
74: <a href="http://arxiv.org/abs/1503.05261"> arxiv:1503.05261 </a>
75:
76: <li> T.Koyama, A.Takemura,
77: Holonomic gradient method for distribution function of a weighted sum
78: of noncentral chi-square random variables,
79: <a href="http://arxiv.org/abs/1503.00378"> arxiv:1503.00378 </a>
80:
81: <li> Y.Goto,
82: Contiguity relations of Lauricella's F_D revisited,
83: <a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a>
1.12 takayama 84:
1.15 takayama 85: <li>
86: T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama,
87: Software Packages for Holonomic Gradient Method,
88: Mathematial Software --- ICMS 2014,
89: 4th International Conference, Proceedings.
90: Edited by Hoon Hong and Chee Yap,
91: Springer lecture notes in computer science 8592,
92: 706--712.
93: <a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_105">
94: DOI
95: </a>
96:
1.11 takayama 97: <li>N.Marumo, T.Oaku, A.Takemura,
98: Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
99: <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
100:
1.8 takayama 101: <li> J.Hayakawa, A.Takemura,
102: Estimation of exponential-polynomial distribution by holonomic gradient descent
103: <a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
104:
105: <li> C.Siriteanu, A.Takemura, S.Kuriki,
106: MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
107: <a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
108:
1.4 takayama 109: <li> T.Koyama,
1.1 takayama 110: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
111: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
112:
113: <li> T.Hibi, K.Nishiyama, N.Takayama,
114: Pfaffian Systems of A-Hypergeometric Equations I,
115: Bases of Twisted Cohomology Groups,
116: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
1.22 takayama 117: (major revision v2 of arxiv:1212.6103).
118: Accepted version is at
119: <a href="http://dx.doi.org/10.1016/j.aim.2016.10.021"> DOI </a>
1.1 takayama 120:
121: <li> <img src="./wakaba01.png" alt="Intro">
122: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
123: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
124:
125: <li> <img src="./wakaba01.png" alt="Intro">
126: Introduction to the Holonomic Gradient Method (movie), 2013.
127: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
128:
1.2 takayama 129:
1.1 takayama 130: <li> T.Sei, A.Kume,
1.2 takayama 131: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1 takayama 132: Statistics and Computing, 2013,
133: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
134:
1.4 takayama 135: <li> T.Koyama, A.Takemura,
1.2 takayama 136: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
137: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
138:
1.1 takayama 139: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
140: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
141: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
1.11 takayama 142: Journal of Pure and Applied Algebra (online),
143: <a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
1.1 takayama 144:
145: <li>
146: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
147: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
148: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
149: Computational Statistics (2013)
150: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
151:
152: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
153: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
154: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
155: Journal of Multivariate Analysis, 117, (2013) 296-312,
156: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
157:
158: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
159: Properties and applications of Fisher distribution on the rotation group,
160: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
161: Journal of Multivariate Analysis, 116 (2013), 440--455,
162: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
163:
164: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
165: Funkcialaj Ekvacioj 56 (2013), 51--61.
1.11 takayama 166: <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
167: <!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
1.1 takayama 168:
169: <li>
170: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
171: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
172: Holonomic Gradient Descent and its Application to Fisher-Bingham Integral,
173: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> -->
174: Advances in Applied Mathematics 47 (2011), 639--658,
175: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
1.13 takayama 176:
1.1 takayama 177: </ol>
178:
1.13 takayama 179: Early papers related to HGM. <br>
180: <ol>
181: <li>
182: H.Dwinwoodie, L.Matusevich, E. Mosteig,
183: Transform methods for the hypergeometric distribution,
184: Statistics and Computing 14 (2004), 287--297.
185: </ol>
186:
187:
188:
1.2 takayama 189: <h2> Three Steps of HGM </h2>
190: <ol>
1.10 takayama 191: <li> Finding a holonomic system satisfied by the normalizing constant.
1.2 takayama 192: We may use computational or theoretical methods to find it.
193: Groebner basis and related methods are used.
1.10 takayama 194: <li> Finding an initial value vector for the holonomic system.
1.2 takayama 195: This is equivalent to evaluating the normalizing constant and its derivatives
196: at a point.
197: This step is usually performed by a series expansion.
1.10 takayama 198: <li> Solving the holonomic system numerically. We use several methods
1.2 takayama 199: in numerical analysis such as the Runge-Kutta method of solving
200: ordinary differential equations and efficient solvers of systems of linear
201: equations.
202: </ol>
203:
1.1 takayama 204: <h2> Software Packages for HGM</h2>
1.14 takayama 205:
1.15 takayama 206: <ul>
207: <li>
1.16 takayama 208: CRAN package <a href="https://cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).
1.14 takayama 209:
1.15 takayama 210: <li>
1.14 takayama 211: Some software packages are experimental and temporary documents are found in
1.6 takayama 212: "asir-contrib manual" (auto-autogenerated part), or
213: "Experimental Functions in Asir", or "miscellaneous and other documents"
214: of the
215: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7 takayama 216: OpenXM documents</a>
1.8 takayama 217: or in <a href="./"> this folder</a>.
1.10 takayama 218: The nightly snapshot of the asir-contrib can be found in the asir page below,
1.6 takayama 219: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8 takayama 220: cvsweb page</a>.
1.1 takayama 221: <ol>
1.9 takayama 222: <li> Command line interfaces are in the folder OpenXM/src/hgm
223: in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
224: OpenXM distribution page </a>.
1.14 takayama 225: <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 226: To install this package in R, type in
227: <pre>
228: R CMD install hgm_*.tar.gz
229: </pre>
1.10 takayama 230: <li> The following packages are
231: for the computer algebra system
232: <a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
233: They are in the asir-contrib collection.
234: <ul>
235: <li> yang.rr (for Pfaffian systems) ,
236: nk_restriction.rr (for D-module integrations),
237: tk_jack.rr (for Jack polynomials),
238: ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
239: are for the steps 1 or 2.
240: <li> nk_fb_gen_c.rr is a package to generate a C program to perform
1.7 takayama 241: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.10 takayama 242: <li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
243: </ul>
1.1 takayama 244: </ol>
245:
1.15 takayama 246: </ul>
247:
1.1 takayama 248: <h2> Programs to try examples of our papers </h2>
249: <ol>
250: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
251: </ol>
252:
1.24 ! takayama 253: <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.23 2017/07/12 01:32:58 takayama Exp $ </pre>
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