Annotation of OpenXM/src/hgm/doc/ref-hgm.html, Revision 1.22
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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>
1.22 ! takayama 108: (major revision v2 of arxiv:1212.6103).
! 109: Accepted version is at
! 110: <a href="http://dx.doi.org/10.1016/j.aim.2016.10.021"> DOI </a>
1.1 takayama 111:
112: <li> <img src="./wakaba01.png" alt="Intro">
113: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
114: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
115:
116: <li> <img src="./wakaba01.png" alt="Intro">
117: Introduction to the Holonomic Gradient Method (movie), 2013.
118: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
119:
1.2 takayama 120:
1.1 takayama 121: <li> T.Sei, A.Kume,
1.2 takayama 122: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1 takayama 123: Statistics and Computing, 2013,
124: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
125:
1.4 takayama 126: <li> T.Koyama, A.Takemura,
1.2 takayama 127: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
128: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
129:
1.1 takayama 130: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
131: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
132: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
1.11 takayama 133: Journal of Pure and Applied Algebra (online),
134: <a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
1.1 takayama 135:
136: <li>
137: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
138: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
139: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
140: Computational Statistics (2013)
141: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
142:
143: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
144: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
145: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
146: Journal of Multivariate Analysis, 117, (2013) 296-312,
147: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
148:
149: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
150: Properties and applications of Fisher distribution on the rotation group,
151: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
152: Journal of Multivariate Analysis, 116 (2013), 440--455,
153: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
154:
155: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
156: Funkcialaj Ekvacioj 56 (2013), 51--61.
1.11 takayama 157: <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
158: <!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
1.1 takayama 159:
160: <li>
161: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
162: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
163: Holonomic Gradient Descent and its Application to Fisher-Bingham Integral,
164: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> -->
165: Advances in Applied Mathematics 47 (2011), 639--658,
166: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
1.13 takayama 167:
1.1 takayama 168: </ol>
169:
1.13 takayama 170: Early papers related to HGM. <br>
171: <ol>
172: <li>
173: H.Dwinwoodie, L.Matusevich, E. Mosteig,
174: Transform methods for the hypergeometric distribution,
175: Statistics and Computing 14 (2004), 287--297.
176: </ol>
177:
178:
179:
1.2 takayama 180: <h2> Three Steps of HGM </h2>
181: <ol>
1.10 takayama 182: <li> Finding a holonomic system satisfied by the normalizing constant.
1.2 takayama 183: We may use computational or theoretical methods to find it.
184: Groebner basis and related methods are used.
1.10 takayama 185: <li> Finding an initial value vector for the holonomic system.
1.2 takayama 186: This is equivalent to evaluating the normalizing constant and its derivatives
187: at a point.
188: This step is usually performed by a series expansion.
1.10 takayama 189: <li> Solving the holonomic system numerically. We use several methods
1.2 takayama 190: in numerical analysis such as the Runge-Kutta method of solving
191: ordinary differential equations and efficient solvers of systems of linear
192: equations.
193: </ol>
194:
1.1 takayama 195: <h2> Software Packages for HGM</h2>
1.14 takayama 196:
1.15 takayama 197: <ul>
198: <li>
1.16 takayama 199: CRAN package <a href="https://cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).
1.14 takayama 200:
1.15 takayama 201: <li>
1.14 takayama 202: Some software packages are experimental and temporary documents are found in
1.6 takayama 203: "asir-contrib manual" (auto-autogenerated part), or
204: "Experimental Functions in Asir", or "miscellaneous and other documents"
205: of the
206: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7 takayama 207: OpenXM documents</a>
1.8 takayama 208: or in <a href="./"> this folder</a>.
1.10 takayama 209: The nightly snapshot of the asir-contrib can be found in the asir page below,
1.6 takayama 210: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8 takayama 211: cvsweb page</a>.
1.1 takayama 212: <ol>
1.9 takayama 213: <li> Command line interfaces are in the folder OpenXM/src/hgm
214: in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
215: OpenXM distribution page </a>.
1.14 takayama 216: <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 217: To install this package in R, type in
218: <pre>
219: R CMD install hgm_*.tar.gz
220: </pre>
1.10 takayama 221: <li> The following packages are
222: for the computer algebra system
223: <a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
224: They are in the asir-contrib collection.
225: <ul>
226: <li> yang.rr (for Pfaffian systems) ,
227: nk_restriction.rr (for D-module integrations),
228: tk_jack.rr (for Jack polynomials),
229: ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
230: are for the steps 1 or 2.
231: <li> nk_fb_gen_c.rr is a package to generate a C program to perform
1.7 takayama 232: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.10 takayama 233: <li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
234: </ul>
1.1 takayama 235: </ol>
236:
1.15 takayama 237: </ul>
238:
1.1 takayama 239: <h2> Programs to try examples of our papers </h2>
240: <ol>
241: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
242: </ol>
243:
1.22 ! takayama 244: <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.21 2016/11/03 23:05:22 takayama Exp $ </pre>
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