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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>
1.23 ! takayama 15: <li> F.H.Danufane, K.Ohara, N.Takayama,
! 16: Holonomic Gradient Method for the Distribution Function of the Largest Root of Complex Non-central Wishart Matrices,
! 17: <a href="https://arxiv.org/abs/1707.02564"> arxiv:1707.02564 </a>
! 18: <li> T.Koyama,
! 19: An integral formula for the powered sum of the independent, identically and normally distributed random variables,
! 20: <a href="https://arxiv.org/abs/1706.03989"> arxiv:1706.03989 </a>
1.21 takayama 21: <li> H.Hashiguchi, N.Takayama, A.Takemura,
22: Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability
23: by Holonomic Gradient Method,
24: <a href="https://arxiv.org/abs/1610.09187"> arxiv:1610.09187 </a>
25:
1.18 takayama 26: <li> R.Vidunas, A.Takemura,
27: Differential relations for the largest root distribution
28: of complex non-central Wishart matrices,
29: <a href="http://arxiv.org/abs/1609.01799"> arxiv:1609.01799 </a>
30:
1.20 takayama 31: <li> S.Mano,
32: The A-hypergeometric System Associated with the Rational Normal Curve and
33: Exchangeable Structures,
34: <a href="http://arxiv.org/abs/1607.03569"> arxiv:1607.03569 </a>
35:
1.19 takayama 36: <li> M.Noro,
37: System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions,
38: <a href="http://dl.acm.org/citation.cfm?doid=2930889.2930905"> ACM DL </a>
39:
1.12 takayama 40: <li> Y.Goto, K.Matsumoto,
41: Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications,
1.13 takayama 42: <a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637 </a>
43:
44: <li> T.Koyama,
45: Holonomic gradient method for the probability content of a simplex
46: region
47: with a multivariate normal distribution,
48: <a href="http://arxiv.org/abs/1512.06564"> arxiv:1512.06564 </a>
49:
50:
51: <li> N.Takayama, S.Kuriki, A.Takemura,
52: A-Hpergeometric Distributions and Newton Polytopes,
53: <a href="http://arxiv.org/abs/1510.02269"> arxiv:1510.02269 </a>
54:
55: <li> G.Weyenberg, R.Yoshida, D.Howe,
56: Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace,
57: <a href="http://arxiv.org/abs/1506.00142"> arxiv:1506.00142 </a>
58:
1.17 takayama 59: <li> C.Siriteanu, A.Takemura, C.Koutschan, S.Kuriki, D.St.P.Richards, H.Sin,
60: Exact ZF Analysis and Computer-Algebra-Aided Evaluation
61: in Rank-1 LoS Rician Fading,
62: <a href="http://arxiv.org/abs/1507.07056"> arxiv:1507.07056 </a>
63:
1.13 takayama 64: <li> K.Ohara, N.Takayama,
65: Pfaffian Systems of A-Hypergeometric Systems II ---
66: Holonomic Gradient Method,
67: <a href="http://arxiv.org/abs/1505.02947"> arxiv:1505.02947 </a>
68:
69: <li> T.Koyama,
70: The Annihilating Ideal of the Fisher Integral,
71: <a href="http://arxiv.org/abs/1503.05261"> arxiv:1503.05261 </a>
72:
73: <li> T.Koyama, A.Takemura,
74: Holonomic gradient method for distribution function of a weighted sum
75: of noncentral chi-square random variables,
76: <a href="http://arxiv.org/abs/1503.00378"> arxiv:1503.00378 </a>
77:
78: <li> Y.Goto,
79: Contiguity relations of Lauricella's F_D revisited,
80: <a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a>
1.12 takayama 81:
1.15 takayama 82: <li>
83: T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama,
84: Software Packages for Holonomic Gradient Method,
85: Mathematial Software --- ICMS 2014,
86: 4th International Conference, Proceedings.
87: Edited by Hoon Hong and Chee Yap,
88: Springer lecture notes in computer science 8592,
89: 706--712.
90: <a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_105">
91: DOI
92: </a>
93:
1.11 takayama 94: <li>N.Marumo, T.Oaku, A.Takemura,
95: Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
96: <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
97:
1.8 takayama 98: <li> J.Hayakawa, A.Takemura,
99: Estimation of exponential-polynomial distribution by holonomic gradient descent
100: <a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
101:
102: <li> C.Siriteanu, A.Takemura, S.Kuriki,
103: MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
104: <a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
105:
1.4 takayama 106: <li> T.Koyama,
1.1 takayama 107: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
108: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
109:
110: <li> T.Hibi, K.Nishiyama, N.Takayama,
111: Pfaffian Systems of A-Hypergeometric Equations I,
112: Bases of Twisted Cohomology Groups,
113: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
1.22 takayama 114: (major revision v2 of arxiv:1212.6103).
115: Accepted version is at
116: <a href="http://dx.doi.org/10.1016/j.aim.2016.10.021"> DOI </a>
1.1 takayama 117:
118: <li> <img src="./wakaba01.png" alt="Intro">
119: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
120: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
121:
122: <li> <img src="./wakaba01.png" alt="Intro">
123: Introduction to the Holonomic Gradient Method (movie), 2013.
124: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
125:
1.2 takayama 126:
1.1 takayama 127: <li> T.Sei, A.Kume,
1.2 takayama 128: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1 takayama 129: Statistics and Computing, 2013,
130: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
131:
1.4 takayama 132: <li> T.Koyama, A.Takemura,
1.2 takayama 133: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
134: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
135:
1.1 takayama 136: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
137: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
138: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
1.11 takayama 139: Journal of Pure and Applied Algebra (online),
140: <a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
1.1 takayama 141:
142: <li>
143: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
144: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
145: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
146: Computational Statistics (2013)
147: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
148:
149: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
150: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
151: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
152: Journal of Multivariate Analysis, 117, (2013) 296-312,
153: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
154:
155: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
156: Properties and applications of Fisher distribution on the rotation group,
157: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
158: Journal of Multivariate Analysis, 116 (2013), 440--455,
159: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
160:
161: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
162: Funkcialaj Ekvacioj 56 (2013), 51--61.
1.11 takayama 163: <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
164: <!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
1.1 takayama 165:
166: <li>
167: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
168: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
169: Holonomic Gradient Descent and its Application to Fisher-Bingham Integral,
170: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> -->
171: Advances in Applied Mathematics 47 (2011), 639--658,
172: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
1.13 takayama 173:
1.1 takayama 174: </ol>
175:
1.13 takayama 176: Early papers related to HGM. <br>
177: <ol>
178: <li>
179: H.Dwinwoodie, L.Matusevich, E. Mosteig,
180: Transform methods for the hypergeometric distribution,
181: Statistics and Computing 14 (2004), 287--297.
182: </ol>
183:
184:
185:
1.2 takayama 186: <h2> Three Steps of HGM </h2>
187: <ol>
1.10 takayama 188: <li> Finding a holonomic system satisfied by the normalizing constant.
1.2 takayama 189: We may use computational or theoretical methods to find it.
190: Groebner basis and related methods are used.
1.10 takayama 191: <li> Finding an initial value vector for the holonomic system.
1.2 takayama 192: This is equivalent to evaluating the normalizing constant and its derivatives
193: at a point.
194: This step is usually performed by a series expansion.
1.10 takayama 195: <li> Solving the holonomic system numerically. We use several methods
1.2 takayama 196: in numerical analysis such as the Runge-Kutta method of solving
197: ordinary differential equations and efficient solvers of systems of linear
198: equations.
199: </ol>
200:
1.1 takayama 201: <h2> Software Packages for HGM</h2>
1.14 takayama 202:
1.15 takayama 203: <ul>
204: <li>
1.16 takayama 205: CRAN package <a href="https://cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).
1.14 takayama 206:
1.15 takayama 207: <li>
1.14 takayama 208: Some software packages are experimental and temporary documents are found in
1.6 takayama 209: "asir-contrib manual" (auto-autogenerated part), or
210: "Experimental Functions in Asir", or "miscellaneous and other documents"
211: of the
212: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7 takayama 213: OpenXM documents</a>
1.8 takayama 214: or in <a href="./"> this folder</a>.
1.10 takayama 215: The nightly snapshot of the asir-contrib can be found in the asir page below,
1.6 takayama 216: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8 takayama 217: cvsweb page</a>.
1.1 takayama 218: <ol>
1.9 takayama 219: <li> Command line interfaces are in the folder OpenXM/src/hgm
220: in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
221: OpenXM distribution page </a>.
1.14 takayama 222: <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 223: To install this package in R, type in
224: <pre>
225: R CMD install hgm_*.tar.gz
226: </pre>
1.10 takayama 227: <li> The following packages are
228: for the computer algebra system
229: <a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
230: They are in the asir-contrib collection.
231: <ul>
232: <li> yang.rr (for Pfaffian systems) ,
233: nk_restriction.rr (for D-module integrations),
234: tk_jack.rr (for Jack polynomials),
235: ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
236: are for the steps 1 or 2.
237: <li> nk_fb_gen_c.rr is a package to generate a C program to perform
1.7 takayama 238: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.10 takayama 239: <li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
240: </ul>
1.1 takayama 241: </ol>
242:
1.15 takayama 243: </ul>
244:
1.1 takayama 245: <h2> Programs to try examples of our papers </h2>
246: <ol>
247: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
248: </ol>
249:
1.23 ! takayama 250: <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.22 2016/11/03 23:19:18 takayama Exp $ </pre>
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