Annotation of OpenXM/src/hgm/doc/ref-hgm.html, Revision 1.20
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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>
1.18 takayama 15: <li> R.Vidunas, A.Takemura,
16: Differential relations for the largest root distribution
17: of complex non-central Wishart matrices,
18: <a href="http://arxiv.org/abs/1609.01799"> arxiv:1609.01799 </a>
19:
1.20 ! takayama 20: <li> S.Mano,
! 21: The A-hypergeometric System Associated with the Rational Normal Curve and
! 22: Exchangeable Structures,
! 23: <a href="http://arxiv.org/abs/1607.03569"> arxiv:1607.03569 </a>
! 24:
1.19 takayama 25: <li> M.Noro,
26: System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions,
27: <a href="http://dl.acm.org/citation.cfm?doid=2930889.2930905"> ACM DL </a>
28:
1.12 takayama 29: <li> Y.Goto, K.Matsumoto,
30: Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications,
1.13 takayama 31: <a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637 </a>
32:
33: <li> T.Koyama,
34: Holonomic gradient method for the probability content of a simplex
35: region
36: with a multivariate normal distribution,
37: <a href="http://arxiv.org/abs/1512.06564"> arxiv:1512.06564 </a>
38:
39:
40: <li> N.Takayama, S.Kuriki, A.Takemura,
41: A-Hpergeometric Distributions and Newton Polytopes,
42: <a href="http://arxiv.org/abs/1510.02269"> arxiv:1510.02269 </a>
43:
44: <li> G.Weyenberg, R.Yoshida, D.Howe,
45: Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace,
46: <a href="http://arxiv.org/abs/1506.00142"> arxiv:1506.00142 </a>
47:
1.17 takayama 48: <li> C.Siriteanu, A.Takemura, C.Koutschan, S.Kuriki, D.St.P.Richards, H.Sin,
49: Exact ZF Analysis and Computer-Algebra-Aided Evaluation
50: in Rank-1 LoS Rician Fading,
51: <a href="http://arxiv.org/abs/1507.07056"> arxiv:1507.07056 </a>
52:
1.13 takayama 53: <li> K.Ohara, N.Takayama,
54: Pfaffian Systems of A-Hypergeometric Systems II ---
55: Holonomic Gradient Method,
56: <a href="http://arxiv.org/abs/1505.02947"> arxiv:1505.02947 </a>
57:
58: <li> T.Koyama,
59: The Annihilating Ideal of the Fisher Integral,
60: <a href="http://arxiv.org/abs/1503.05261"> arxiv:1503.05261 </a>
61:
62: <li> T.Koyama, A.Takemura,
63: Holonomic gradient method for distribution function of a weighted sum
64: of noncentral chi-square random variables,
65: <a href="http://arxiv.org/abs/1503.00378"> arxiv:1503.00378 </a>
66:
67: <li> Y.Goto,
68: Contiguity relations of Lauricella's F_D revisited,
69: <a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a>
1.12 takayama 70:
1.15 takayama 71: <li>
72: T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama,
73: Software Packages for Holonomic Gradient Method,
74: Mathematial Software --- ICMS 2014,
75: 4th International Conference, Proceedings.
76: Edited by Hoon Hong and Chee Yap,
77: Springer lecture notes in computer science 8592,
78: 706--712.
79: <a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_105">
80: DOI
81: </a>
82:
1.11 takayama 83: <li>N.Marumo, T.Oaku, A.Takemura,
84: Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
85: <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
86:
1.8 takayama 87: <li> J.Hayakawa, A.Takemura,
88: Estimation of exponential-polynomial distribution by holonomic gradient descent
89: <a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
90:
91: <li> C.Siriteanu, A.Takemura, S.Kuriki,
92: MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
93: <a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
94:
1.4 takayama 95: <li> T.Koyama,
1.1 takayama 96: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
97: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
98:
99: <li> T.Hibi, K.Nishiyama, N.Takayama,
100: Pfaffian Systems of A-Hypergeometric Equations I,
101: Bases of Twisted Cohomology Groups,
102: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
103: (major revision v2 of arxiv:1212.6103)
104:
105: <li> <img src="./wakaba01.png" alt="Intro">
106: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
107: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
108:
109: <li> <img src="./wakaba01.png" alt="Intro">
110: Introduction to the Holonomic Gradient Method (movie), 2013.
111: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
112:
1.2 takayama 113:
1.1 takayama 114: <li> T.Sei, A.Kume,
1.2 takayama 115: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1 takayama 116: Statistics and Computing, 2013,
117: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
118:
1.4 takayama 119: <li> T.Koyama, A.Takemura,
1.2 takayama 120: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
121: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
122:
1.1 takayama 123: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
124: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
125: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
1.11 takayama 126: Journal of Pure and Applied Algebra (online),
127: <a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
1.1 takayama 128:
129: <li>
130: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
131: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
132: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
133: Computational Statistics (2013)
134: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
135:
136: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
137: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
138: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
139: Journal of Multivariate Analysis, 117, (2013) 296-312,
140: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
141:
142: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
143: Properties and applications of Fisher distribution on the rotation group,
144: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
145: Journal of Multivariate Analysis, 116 (2013), 440--455,
146: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
147:
148: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
149: Funkcialaj Ekvacioj 56 (2013), 51--61.
1.11 takayama 150: <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
151: <!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
1.1 takayama 152:
153: <li>
154: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
155: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
156: Holonomic Gradient Descent and its Application to Fisher-Bingham Integral,
157: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> -->
158: Advances in Applied Mathematics 47 (2011), 639--658,
159: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
1.13 takayama 160:
1.1 takayama 161: </ol>
162:
1.13 takayama 163: Early papers related to HGM. <br>
164: <ol>
165: <li>
166: H.Dwinwoodie, L.Matusevich, E. Mosteig,
167: Transform methods for the hypergeometric distribution,
168: Statistics and Computing 14 (2004), 287--297.
169: </ol>
170:
171:
172:
1.2 takayama 173: <h2> Three Steps of HGM </h2>
174: <ol>
1.10 takayama 175: <li> Finding a holonomic system satisfied by the normalizing constant.
1.2 takayama 176: We may use computational or theoretical methods to find it.
177: Groebner basis and related methods are used.
1.10 takayama 178: <li> Finding an initial value vector for the holonomic system.
1.2 takayama 179: This is equivalent to evaluating the normalizing constant and its derivatives
180: at a point.
181: This step is usually performed by a series expansion.
1.10 takayama 182: <li> Solving the holonomic system numerically. We use several methods
1.2 takayama 183: in numerical analysis such as the Runge-Kutta method of solving
184: ordinary differential equations and efficient solvers of systems of linear
185: equations.
186: </ol>
187:
1.1 takayama 188: <h2> Software Packages for HGM</h2>
1.14 takayama 189:
1.15 takayama 190: <ul>
191: <li>
1.16 takayama 192: CRAN package <a href="https://cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).
1.14 takayama 193:
1.15 takayama 194: <li>
1.14 takayama 195: Some software packages are experimental and temporary documents are found in
1.6 takayama 196: "asir-contrib manual" (auto-autogenerated part), or
197: "Experimental Functions in Asir", or "miscellaneous and other documents"
198: of the
199: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7 takayama 200: OpenXM documents</a>
1.8 takayama 201: or in <a href="./"> this folder</a>.
1.10 takayama 202: The nightly snapshot of the asir-contrib can be found in the asir page below,
1.6 takayama 203: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8 takayama 204: cvsweb page</a>.
1.1 takayama 205: <ol>
1.9 takayama 206: <li> Command line interfaces are in the folder OpenXM/src/hgm
207: in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
208: OpenXM distribution page </a>.
1.14 takayama 209: <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 210: To install this package in R, type in
211: <pre>
212: R CMD install hgm_*.tar.gz
213: </pre>
1.10 takayama 214: <li> The following packages are
215: for the computer algebra system
216: <a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
217: They are in the asir-contrib collection.
218: <ul>
219: <li> yang.rr (for Pfaffian systems) ,
220: nk_restriction.rr (for D-module integrations),
221: tk_jack.rr (for Jack polynomials),
222: ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
223: are for the steps 1 or 2.
224: <li> nk_fb_gen_c.rr is a package to generate a C program to perform
1.7 takayama 225: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.10 takayama 226: <li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
227: </ul>
1.1 takayama 228: </ol>
229:
1.15 takayama 230: </ul>
231:
1.1 takayama 232: <h2> Programs to try examples of our papers </h2>
233: <ol>
234: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
235: </ol>
236:
1.20 ! takayama 237: <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.19 2016/09/15 02:25:48 takayama Exp $ </pre>
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