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