Annotation of OpenXM/src/hgm/doc/ref-hgm.html, Revision 1.18
1.1 takayama 1: <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//JA" "http://www.w3.org/TR/REC-html40/loose.dtd">
2: <html>
3: <head>
4: <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
5: <title>References for HGM</title> <!-- Use UTF-8 文字 code-->
1.13 takayama 6: <!-- Do not edit this file. Edit it under OpenXM/src/hgm/doc -->
1.1 takayama 7: </head>
8: <body>
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:
1.12 takayama 20: <li> Y.Goto, K.Matsumoto,
21: Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications,
1.13 takayama 22: <a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637 </a>
23:
24: <li> T.Koyama,
25: Holonomic gradient method for the probability content of a simplex
26: region
27: with a multivariate normal distribution,
28: <a href="http://arxiv.org/abs/1512.06564"> arxiv:1512.06564 </a>
29:
30:
31: <li> N.Takayama, S.Kuriki, A.Takemura,
32: A-Hpergeometric Distributions and Newton Polytopes,
33: <a href="http://arxiv.org/abs/1510.02269"> arxiv:1510.02269 </a>
34:
35: <li> G.Weyenberg, R.Yoshida, D.Howe,
36: Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace,
37: <a href="http://arxiv.org/abs/1506.00142"> arxiv:1506.00142 </a>
38:
1.17 takayama 39: <li> C.Siriteanu, A.Takemura, C.Koutschan, S.Kuriki, D.St.P.Richards, H.Sin,
40: Exact ZF Analysis and Computer-Algebra-Aided Evaluation
41: in Rank-1 LoS Rician Fading,
42: <a href="http://arxiv.org/abs/1507.07056"> arxiv:1507.07056 </a>
43:
1.13 takayama 44: <li> K.Ohara, N.Takayama,
45: Pfaffian Systems of A-Hypergeometric Systems II ---
46: Holonomic Gradient Method,
47: <a href="http://arxiv.org/abs/1505.02947"> arxiv:1505.02947 </a>
48:
49: <li> T.Koyama,
50: The Annihilating Ideal of the Fisher Integral,
51: <a href="http://arxiv.org/abs/1503.05261"> arxiv:1503.05261 </a>
52:
53: <li> T.Koyama, A.Takemura,
54: Holonomic gradient method for distribution function of a weighted sum
55: of noncentral chi-square random variables,
56: <a href="http://arxiv.org/abs/1503.00378"> arxiv:1503.00378 </a>
57:
58: <li> Y.Goto,
59: Contiguity relations of Lauricella's F_D revisited,
60: <a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a>
1.12 takayama 61:
1.15 takayama 62: <li>
63: T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama,
64: Software Packages for Holonomic Gradient Method,
65: Mathematial Software --- ICMS 2014,
66: 4th International Conference, Proceedings.
67: Edited by Hoon Hong and Chee Yap,
68: Springer lecture notes in computer science 8592,
69: 706--712.
70: <a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_105">
71: DOI
72: </a>
73:
1.11 takayama 74: <li>N.Marumo, T.Oaku, A.Takemura,
75: Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
76: <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
77:
1.8 takayama 78: <li> J.Hayakawa, A.Takemura,
79: Estimation of exponential-polynomial distribution by holonomic gradient descent
80: <a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
81:
82: <li> C.Siriteanu, A.Takemura, S.Kuriki,
83: MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
84: <a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
85:
1.4 takayama 86: <li> T.Koyama,
1.1 takayama 87: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
88: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
89:
90: <li> T.Hibi, K.Nishiyama, N.Takayama,
91: Pfaffian Systems of A-Hypergeometric Equations I,
92: Bases of Twisted Cohomology Groups,
93: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
94: (major revision v2 of arxiv:1212.6103)
95:
96: <li> <img src="./wakaba01.png" alt="Intro">
97: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
98: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
99:
100: <li> <img src="./wakaba01.png" alt="Intro">
101: Introduction to the Holonomic Gradient Method (movie), 2013.
102: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
103:
1.2 takayama 104:
1.1 takayama 105: <li> T.Sei, A.Kume,
1.2 takayama 106: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1 takayama 107: Statistics and Computing, 2013,
108: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
109:
1.4 takayama 110: <li> T.Koyama, A.Takemura,
1.2 takayama 111: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
112: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
113:
1.1 takayama 114: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
115: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
116: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
1.11 takayama 117: Journal of Pure and Applied Algebra (online),
118: <a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
1.1 takayama 119:
120: <li>
121: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
122: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
123: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
124: Computational Statistics (2013)
125: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
126:
127: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
128: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
129: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
130: Journal of Multivariate Analysis, 117, (2013) 296-312,
131: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
132:
133: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
134: Properties and applications of Fisher distribution on the rotation group,
135: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
136: Journal of Multivariate Analysis, 116 (2013), 440--455,
137: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
138:
139: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
140: Funkcialaj Ekvacioj 56 (2013), 51--61.
1.11 takayama 141: <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
142: <!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
1.1 takayama 143:
144: <li>
145: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
146: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
147: Holonomic Gradient Descent and its Application to Fisher-Bingham Integral,
148: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> -->
149: Advances in Applied Mathematics 47 (2011), 639--658,
150: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
1.13 takayama 151:
1.1 takayama 152: </ol>
153:
1.13 takayama 154: Early papers related to HGM. <br>
155: <ol>
156: <li>
157: H.Dwinwoodie, L.Matusevich, E. Mosteig,
158: Transform methods for the hypergeometric distribution,
159: Statistics and Computing 14 (2004), 287--297.
160: </ol>
161:
162:
163:
1.2 takayama 164: <h2> Three Steps of HGM </h2>
165: <ol>
1.10 takayama 166: <li> Finding a holonomic system satisfied by the normalizing constant.
1.2 takayama 167: We may use computational or theoretical methods to find it.
168: Groebner basis and related methods are used.
1.10 takayama 169: <li> Finding an initial value vector for the holonomic system.
1.2 takayama 170: This is equivalent to evaluating the normalizing constant and its derivatives
171: at a point.
172: This step is usually performed by a series expansion.
1.10 takayama 173: <li> Solving the holonomic system numerically. We use several methods
1.2 takayama 174: in numerical analysis such as the Runge-Kutta method of solving
175: ordinary differential equations and efficient solvers of systems of linear
176: equations.
177: </ol>
178:
1.1 takayama 179: <h2> Software Packages for HGM</h2>
1.14 takayama 180:
1.15 takayama 181: <ul>
182: <li>
1.16 takayama 183: CRAN package <a href="https://cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).
1.14 takayama 184:
1.15 takayama 185: <li>
1.14 takayama 186: Some software packages are experimental and temporary documents are found in
1.6 takayama 187: "asir-contrib manual" (auto-autogenerated part), or
188: "Experimental Functions in Asir", or "miscellaneous and other documents"
189: of the
190: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7 takayama 191: OpenXM documents</a>
1.8 takayama 192: or in <a href="./"> this folder</a>.
1.10 takayama 193: The nightly snapshot of the asir-contrib can be found in the asir page below,
1.6 takayama 194: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8 takayama 195: cvsweb page</a>.
1.1 takayama 196: <ol>
1.9 takayama 197: <li> Command line interfaces are in the folder OpenXM/src/hgm
198: in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
199: OpenXM distribution page </a>.
1.14 takayama 200: <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 201: To install this package in R, type in
202: <pre>
203: R CMD install hgm_*.tar.gz
204: </pre>
1.10 takayama 205: <li> The following packages are
206: for the computer algebra system
207: <a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
208: They are in the asir-contrib collection.
209: <ul>
210: <li> yang.rr (for Pfaffian systems) ,
211: nk_restriction.rr (for D-module integrations),
212: tk_jack.rr (for Jack polynomials),
213: ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
214: are for the steps 1 or 2.
215: <li> nk_fb_gen_c.rr is a package to generate a C program to perform
1.7 takayama 216: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.10 takayama 217: <li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
218: </ul>
1.1 takayama 219: </ol>
220:
1.15 takayama 221: </ul>
222:
1.1 takayama 223: <h2> Programs to try examples of our papers </h2>
224: <ol>
225: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
226: </ol>
227:
1.18 ! takayama 228: <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.17 2016/04/30 11:15:58 takayama Exp $ </pre>
1.1 takayama 229: </body>
230: </html>
FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>
![[BACK]](/icons/cvsweb/back.gif){kind=icon}
Return to ref-hgm.html CVS log ![[TXT]](/icons/cvsweb/text.gif){kind=icon}
![[DIR]](/icons/cvsweb/dir.gif){kind=icon}
Up to [local] / OpenXM / src / hgm / doc