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