Annotation of OpenXM/src/hgm/doc/ref-hgm.html, Revision 1.28
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1.1 takayama 7: <title>References for HGM</title> <!-- Use UTF-8 文字 code-->
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10: <body>
11:
12: <h1> References for the Holonomic Gradient Method (HGM) and
13: the Holonomic Gradient Descent Method (HGD) </h1>
14:
15: <h2> Papers and Tutorials</h2>
16: <ol>
1.28 ! takayama 17: <li>
! 18: N.Takayama, L.Jiu, S.Kuriki, Y.Zhang,
! 19: Computations of the Expected Euler Characteristic for the Largest Eigenvalue of a Real Wishart Matrix,
! 20: <a href="https://arxiv.org/abs/1903.10099"> arxiv:1903.10099 </a>
1.27 takayama 21: <li> M.Harkonen, T.Sei, Y.Hirose,
22: Holonomic extended least angle regression,
23: <a href="https://arxiv.org/abs/1809.08190"> arxiv:1809.08190 </a>
24: <li> S.Mano,
25: Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics,
26: <a href="https://www.springer.com/jp/book/9784431558866">
27: JSS Research Series in Statistics</a>, 2018.
1.26 takayama 28: <li> A.Kume, T.Sei,
29: On the exact maximum likelihood inference of Fisher–Bingham distributions using an adjusted holonomic gradient method,
30: <a href="https://doi.org/10.1007/s11222-017-9765-3"> doi </a> (2018)
1.24 takayama 31: <li> Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama, Nobuki Takayama,
32: Holonomic Gradient Method for Two Way Contingency Tables,
1.25 takayama 33: <a href="https://arxiv.org/abs/1803.04170"> arxiv:1803.04170 </a>
34: <li> F.H.Danufane, K.Ohara, N.Takayama, C.Siriteanu,
35: Holonomic Gradient Method-Based CDF Evaluation for the Largest Eigenvalue of a Complex Noncentral Wishart Matrix
36: (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 37: <a href="https://arxiv.org/abs/1707.02564"> arxiv:1707.02564 </a>
38: <li> T.Koyama,
39: An integral formula for the powered sum of the independent, identically and normally distributed random variables,
40: <a href="https://arxiv.org/abs/1706.03989"> arxiv:1706.03989 </a>
1.21 takayama 41: <li> H.Hashiguchi, N.Takayama, A.Takemura,
42: Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability
43: by Holonomic Gradient Method,
44: <a href="https://arxiv.org/abs/1610.09187"> arxiv:1610.09187 </a>
45:
1.18 takayama 46: <li> R.Vidunas, A.Takemura,
47: Differential relations for the largest root distribution
48: of complex non-central Wishart matrices,
49: <a href="http://arxiv.org/abs/1609.01799"> arxiv:1609.01799 </a>
50:
1.20 takayama 51: <li> S.Mano,
52: The A-hypergeometric System Associated with the Rational Normal Curve and
53: Exchangeable Structures,
54: <a href="http://arxiv.org/abs/1607.03569"> arxiv:1607.03569 </a>
55:
1.19 takayama 56: <li> M.Noro,
57: System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions,
58: <a href="http://dl.acm.org/citation.cfm?doid=2930889.2930905"> ACM DL </a>
59:
1.12 takayama 60: <li> Y.Goto, K.Matsumoto,
61: Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications,
1.13 takayama 62: <a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637 </a>
63:
64: <li> T.Koyama,
65: Holonomic gradient method for the probability content of a simplex
66: region
67: with a multivariate normal distribution,
68: <a href="http://arxiv.org/abs/1512.06564"> arxiv:1512.06564 </a>
69:
70:
71: <li> N.Takayama, S.Kuriki, A.Takemura,
72: A-Hpergeometric Distributions and Newton Polytopes,
73: <a href="http://arxiv.org/abs/1510.02269"> arxiv:1510.02269 </a>
74:
75: <li> G.Weyenberg, R.Yoshida, D.Howe,
76: Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace,
77: <a href="http://arxiv.org/abs/1506.00142"> arxiv:1506.00142 </a>
78:
1.17 takayama 79: <li> C.Siriteanu, A.Takemura, C.Koutschan, S.Kuriki, D.St.P.Richards, H.Sin,
80: Exact ZF Analysis and Computer-Algebra-Aided Evaluation
81: in Rank-1 LoS Rician Fading,
82: <a href="http://arxiv.org/abs/1507.07056"> arxiv:1507.07056 </a>
83:
1.13 takayama 84: <li> K.Ohara, N.Takayama,
85: Pfaffian Systems of A-Hypergeometric Systems II ---
86: Holonomic Gradient Method,
87: <a href="http://arxiv.org/abs/1505.02947"> arxiv:1505.02947 </a>
88:
89: <li> T.Koyama,
90: The Annihilating Ideal of the Fisher Integral,
91: <a href="http://arxiv.org/abs/1503.05261"> arxiv:1503.05261 </a>
92:
93: <li> T.Koyama, A.Takemura,
94: Holonomic gradient method for distribution function of a weighted sum
95: of noncentral chi-square random variables,
96: <a href="http://arxiv.org/abs/1503.00378"> arxiv:1503.00378 </a>
97:
98: <li> Y.Goto,
99: Contiguity relations of Lauricella's F_D revisited,
100: <a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a>
1.12 takayama 101:
1.15 takayama 102: <li>
103: T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama,
104: Software Packages for Holonomic Gradient Method,
105: Mathematial Software --- ICMS 2014,
106: 4th International Conference, Proceedings.
107: Edited by Hoon Hong and Chee Yap,
108: Springer lecture notes in computer science 8592,
109: 706--712.
110: <a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_105">
111: DOI
112: </a>
113:
1.11 takayama 114: <li>N.Marumo, T.Oaku, A.Takemura,
115: Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
116: <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
117:
1.8 takayama 118: <li> J.Hayakawa, A.Takemura,
119: Estimation of exponential-polynomial distribution by holonomic gradient descent
120: <a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
121:
122: <li> C.Siriteanu, A.Takemura, S.Kuriki,
123: MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
124: <a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
125:
1.4 takayama 126: <li> T.Koyama,
1.1 takayama 127: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
128: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
129:
130: <li> T.Hibi, K.Nishiyama, N.Takayama,
131: Pfaffian Systems of A-Hypergeometric Equations I,
132: Bases of Twisted Cohomology Groups,
133: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
1.22 takayama 134: (major revision v2 of arxiv:1212.6103).
135: Accepted version is at
136: <a href="http://dx.doi.org/10.1016/j.aim.2016.10.021"> DOI </a>
1.1 takayama 137:
138: <li> <img src="./wakaba01.png" alt="Intro">
139: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
140: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
141:
142: <li> <img src="./wakaba01.png" alt="Intro">
143: Introduction to the Holonomic Gradient Method (movie), 2013.
144: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
145:
1.2 takayama 146:
1.1 takayama 147: <li> T.Sei, A.Kume,
1.2 takayama 148: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1 takayama 149: Statistics and Computing, 2013,
150: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
151:
1.4 takayama 152: <li> T.Koyama, A.Takemura,
1.2 takayama 153: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
154: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
155:
1.1 takayama 156: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
157: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
158: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
1.11 takayama 159: Journal of Pure and Applied Algebra (online),
160: <a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
1.1 takayama 161:
162: <li>
163: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
164: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
165: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
166: Computational Statistics (2013)
167: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
168:
169: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
170: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
171: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
172: Journal of Multivariate Analysis, 117, (2013) 296-312,
173: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
174:
175: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
176: Properties and applications of Fisher distribution on the rotation group,
177: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
178: Journal of Multivariate Analysis, 116 (2013), 440--455,
179: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
180:
181: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
182: Funkcialaj Ekvacioj 56 (2013), 51--61.
1.11 takayama 183: <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
184: <!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
1.1 takayama 185:
186: <li>
187: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
188: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
189: Holonomic Gradient Descent and its Application to Fisher-Bingham Integral,
190: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> -->
191: Advances in Applied Mathematics 47 (2011), 639--658,
192: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
1.13 takayama 193:
1.1 takayama 194: </ol>
195:
1.13 takayama 196: Early papers related to HGM. <br>
197: <ol>
198: <li>
199: H.Dwinwoodie, L.Matusevich, E. Mosteig,
200: Transform methods for the hypergeometric distribution,
201: Statistics and Computing 14 (2004), 287--297.
202: </ol>
203:
204:
205:
1.2 takayama 206: <h2> Three Steps of HGM </h2>
207: <ol>
1.10 takayama 208: <li> Finding a holonomic system satisfied by the normalizing constant.
1.2 takayama 209: We may use computational or theoretical methods to find it.
210: Groebner basis and related methods are used.
1.10 takayama 211: <li> Finding an initial value vector for the holonomic system.
1.2 takayama 212: This is equivalent to evaluating the normalizing constant and its derivatives
213: at a point.
214: This step is usually performed by a series expansion.
1.10 takayama 215: <li> Solving the holonomic system numerically. We use several methods
1.2 takayama 216: in numerical analysis such as the Runge-Kutta method of solving
217: ordinary differential equations and efficient solvers of systems of linear
218: equations.
219: </ol>
220:
1.1 takayama 221: <h2> Software Packages for HGM</h2>
1.14 takayama 222:
1.15 takayama 223: <ul>
224: <li>
1.16 takayama 225: CRAN package <a href="https://cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).
1.14 takayama 226:
1.15 takayama 227: <li>
1.14 takayama 228: Some software packages are experimental and temporary documents are found in
1.6 takayama 229: "asir-contrib manual" (auto-autogenerated part), or
230: "Experimental Functions in Asir", or "miscellaneous and other documents"
231: of the
232: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7 takayama 233: OpenXM documents</a>
1.8 takayama 234: or in <a href="./"> this folder</a>.
1.10 takayama 235: The nightly snapshot of the asir-contrib can be found in the asir page below,
1.6 takayama 236: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8 takayama 237: cvsweb page</a>.
1.1 takayama 238: <ol>
1.9 takayama 239: <li> Command line interfaces are in the folder OpenXM/src/hgm
240: in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
241: OpenXM distribution page </a>.
1.14 takayama 242: <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 243: To install this package in R, type in
244: <pre>
245: R CMD install hgm_*.tar.gz
246: </pre>
1.10 takayama 247: <li> The following packages are
248: for the computer algebra system
249: <a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
250: They are in the asir-contrib collection.
251: <ul>
252: <li> yang.rr (for Pfaffian systems) ,
253: nk_restriction.rr (for D-module integrations),
254: tk_jack.rr (for Jack polynomials),
255: ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
256: are for the steps 1 or 2.
257: <li> nk_fb_gen_c.rr is a package to generate a C program to perform
1.7 takayama 258: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.10 takayama 259: <li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
260: </ul>
1.1 takayama 261: </ol>
262:
1.15 takayama 263: </ul>
264:
1.1 takayama 265: <h2> Programs to try examples of our papers </h2>
266: <ol>
267: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
268: </ol>
269:
1.28 ! takayama 270: <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.27 2018/11/13 01:14:49 takayama Exp $ </pre>
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