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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>
1.26 ! takayama 15: <li> A.Kume, T.Sei,
! 16: On the exact maximum likelihood inference of Fisher–Bingham distributions using an adjusted holonomic gradient method,
! 17: <a href="https://doi.org/10.1007/s11222-017-9765-3"> doi </a> (2018)
1.24 takayama 18: <li> Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama, Nobuki Takayama,
19: Holonomic Gradient Method for Two Way Contingency Tables,
1.25 takayama 20: <a href="https://arxiv.org/abs/1803.04170"> arxiv:1803.04170 </a>
21: <li> F.H.Danufane, K.Ohara, N.Takayama, C.Siriteanu,
22: Holonomic Gradient Method-Based CDF Evaluation for the Largest Eigenvalue of a Complex Noncentral Wishart Matrix
23: (Title of the version 1: Holonomic Gradient Method for the Distribution Function of the Largest Root of Complex Non-central Wishart Matrices),
1.23 takayama 24: <a href="https://arxiv.org/abs/1707.02564"> arxiv:1707.02564 </a>
25: <li> T.Koyama,
26: An integral formula for the powered sum of the independent, identically and normally distributed random variables,
27: <a href="https://arxiv.org/abs/1706.03989"> arxiv:1706.03989 </a>
1.21 takayama 28: <li> H.Hashiguchi, N.Takayama, A.Takemura,
29: Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability
30: by Holonomic Gradient Method,
31: <a href="https://arxiv.org/abs/1610.09187"> arxiv:1610.09187 </a>
32:
1.18 takayama 33: <li> R.Vidunas, A.Takemura,
34: Differential relations for the largest root distribution
35: of complex non-central Wishart matrices,
36: <a href="http://arxiv.org/abs/1609.01799"> arxiv:1609.01799 </a>
37:
1.20 takayama 38: <li> S.Mano,
39: The A-hypergeometric System Associated with the Rational Normal Curve and
40: Exchangeable Structures,
41: <a href="http://arxiv.org/abs/1607.03569"> arxiv:1607.03569 </a>
42:
1.19 takayama 43: <li> M.Noro,
44: System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions,
45: <a href="http://dl.acm.org/citation.cfm?doid=2930889.2930905"> ACM DL </a>
46:
1.12 takayama 47: <li> Y.Goto, K.Matsumoto,
48: Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications,
1.13 takayama 49: <a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637 </a>
50:
51: <li> T.Koyama,
52: Holonomic gradient method for the probability content of a simplex
53: region
54: with a multivariate normal distribution,
55: <a href="http://arxiv.org/abs/1512.06564"> arxiv:1512.06564 </a>
56:
57:
58: <li> N.Takayama, S.Kuriki, A.Takemura,
59: A-Hpergeometric Distributions and Newton Polytopes,
60: <a href="http://arxiv.org/abs/1510.02269"> arxiv:1510.02269 </a>
61:
62: <li> G.Weyenberg, R.Yoshida, D.Howe,
63: Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace,
64: <a href="http://arxiv.org/abs/1506.00142"> arxiv:1506.00142 </a>
65:
1.17 takayama 66: <li> C.Siriteanu, A.Takemura, C.Koutschan, S.Kuriki, D.St.P.Richards, H.Sin,
67: Exact ZF Analysis and Computer-Algebra-Aided Evaluation
68: in Rank-1 LoS Rician Fading,
69: <a href="http://arxiv.org/abs/1507.07056"> arxiv:1507.07056 </a>
70:
1.13 takayama 71: <li> K.Ohara, N.Takayama,
72: Pfaffian Systems of A-Hypergeometric Systems II ---
73: Holonomic Gradient Method,
74: <a href="http://arxiv.org/abs/1505.02947"> arxiv:1505.02947 </a>
75:
76: <li> T.Koyama,
77: The Annihilating Ideal of the Fisher Integral,
78: <a href="http://arxiv.org/abs/1503.05261"> arxiv:1503.05261 </a>
79:
80: <li> T.Koyama, A.Takemura,
81: Holonomic gradient method for distribution function of a weighted sum
82: of noncentral chi-square random variables,
83: <a href="http://arxiv.org/abs/1503.00378"> arxiv:1503.00378 </a>
84:
85: <li> Y.Goto,
86: Contiguity relations of Lauricella's F_D revisited,
87: <a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a>
1.12 takayama 88:
1.15 takayama 89: <li>
90: T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama,
91: Software Packages for Holonomic Gradient Method,
92: Mathematial Software --- ICMS 2014,
93: 4th International Conference, Proceedings.
94: Edited by Hoon Hong and Chee Yap,
95: Springer lecture notes in computer science 8592,
96: 706--712.
97: <a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_105">
98: DOI
99: </a>
100:
1.11 takayama 101: <li>N.Marumo, T.Oaku, A.Takemura,
102: Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
103: <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
104:
1.8 takayama 105: <li> J.Hayakawa, A.Takemura,
106: Estimation of exponential-polynomial distribution by holonomic gradient descent
107: <a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
108:
109: <li> C.Siriteanu, A.Takemura, S.Kuriki,
110: MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
111: <a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
112:
1.4 takayama 113: <li> T.Koyama,
1.1 takayama 114: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
115: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
116:
117: <li> T.Hibi, K.Nishiyama, N.Takayama,
118: Pfaffian Systems of A-Hypergeometric Equations I,
119: Bases of Twisted Cohomology Groups,
120: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
1.22 takayama 121: (major revision v2 of arxiv:1212.6103).
122: Accepted version is at
123: <a href="http://dx.doi.org/10.1016/j.aim.2016.10.021"> DOI </a>
1.1 takayama 124:
125: <li> <img src="./wakaba01.png" alt="Intro">
126: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
127: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
128:
129: <li> <img src="./wakaba01.png" alt="Intro">
130: Introduction to the Holonomic Gradient Method (movie), 2013.
131: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
132:
1.2 takayama 133:
1.1 takayama 134: <li> T.Sei, A.Kume,
1.2 takayama 135: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1 takayama 136: Statistics and Computing, 2013,
137: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
138:
1.4 takayama 139: <li> T.Koyama, A.Takemura,
1.2 takayama 140: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
141: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
142:
1.1 takayama 143: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
144: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
145: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
1.11 takayama 146: Journal of Pure and Applied Algebra (online),
147: <a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
1.1 takayama 148:
149: <li>
150: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
151: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
152: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
153: Computational Statistics (2013)
154: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
155:
156: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
157: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
158: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
159: Journal of Multivariate Analysis, 117, (2013) 296-312,
160: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
161:
162: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
163: Properties and applications of Fisher distribution on the rotation group,
164: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
165: Journal of Multivariate Analysis, 116 (2013), 440--455,
166: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
167:
168: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
169: Funkcialaj Ekvacioj 56 (2013), 51--61.
1.11 takayama 170: <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
171: <!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
1.1 takayama 172:
173: <li>
174: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
175: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
176: Holonomic Gradient Descent and its Application to Fisher-Bingham Integral,
177: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> -->
178: Advances in Applied Mathematics 47 (2011), 639--658,
179: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
1.13 takayama 180:
1.1 takayama 181: </ol>
182:
1.13 takayama 183: Early papers related to HGM. <br>
184: <ol>
185: <li>
186: H.Dwinwoodie, L.Matusevich, E. Mosteig,
187: Transform methods for the hypergeometric distribution,
188: Statistics and Computing 14 (2004), 287--297.
189: </ol>
190:
191:
192:
1.2 takayama 193: <h2> Three Steps of HGM </h2>
194: <ol>
1.10 takayama 195: <li> Finding a holonomic system satisfied by the normalizing constant.
1.2 takayama 196: We may use computational or theoretical methods to find it.
197: Groebner basis and related methods are used.
1.10 takayama 198: <li> Finding an initial value vector for the holonomic system.
1.2 takayama 199: This is equivalent to evaluating the normalizing constant and its derivatives
200: at a point.
201: This step is usually performed by a series expansion.
1.10 takayama 202: <li> Solving the holonomic system numerically. We use several methods
1.2 takayama 203: in numerical analysis such as the Runge-Kutta method of solving
204: ordinary differential equations and efficient solvers of systems of linear
205: equations.
206: </ol>
207:
1.1 takayama 208: <h2> Software Packages for HGM</h2>
1.14 takayama 209:
1.15 takayama 210: <ul>
211: <li>
1.16 takayama 212: CRAN package <a href="https://cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).
1.14 takayama 213:
1.15 takayama 214: <li>
1.14 takayama 215: Some software packages are experimental and temporary documents are found in
1.6 takayama 216: "asir-contrib manual" (auto-autogenerated part), or
217: "Experimental Functions in Asir", or "miscellaneous and other documents"
218: of the
219: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7 takayama 220: OpenXM documents</a>
1.8 takayama 221: or in <a href="./"> this folder</a>.
1.10 takayama 222: The nightly snapshot of the asir-contrib can be found in the asir page below,
1.6 takayama 223: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8 takayama 224: cvsweb page</a>.
1.1 takayama 225: <ol>
1.9 takayama 226: <li> Command line interfaces are in the folder OpenXM/src/hgm
227: in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
228: OpenXM distribution page </a>.
1.14 takayama 229: <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 230: To install this package in R, type in
231: <pre>
232: R CMD install hgm_*.tar.gz
233: </pre>
1.10 takayama 234: <li> The following packages are
235: for the computer algebra system
236: <a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
237: They are in the asir-contrib collection.
238: <ul>
239: <li> yang.rr (for Pfaffian systems) ,
240: nk_restriction.rr (for D-module integrations),
241: tk_jack.rr (for Jack polynomials),
242: ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
243: are for the steps 1 or 2.
244: <li> nk_fb_gen_c.rr is a package to generate a C program to perform
1.7 takayama 245: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.10 takayama 246: <li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
247: </ul>
1.1 takayama 248: </ol>
249:
1.15 takayama 250: </ul>
251:
1.1 takayama 252: <h2> Programs to try examples of our papers </h2>
253: <ol>
254: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
255: </ol>
256:
1.26 ! takayama 257: <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.25 2018/05/07 04:50:46 takayama Exp $ </pre>
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