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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>
1.27 ! takayama 15: <li> M.Harkonen, T.Sei, Y.Hirose,
! 16: Holonomic extended least angle regression,
! 17: <a href="https://arxiv.org/abs/1809.08190"> arxiv:1809.08190 </a>
! 18: <li> S.Mano,
! 19: Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics,
! 20: <a href="https://www.springer.com/jp/book/9784431558866">
! 21: JSS Research Series in Statistics</a>, 2018.
1.26 takayama 22: <li> A.Kume, T.Sei,
23: On the exact maximum likelihood inference of Fisher–Bingham distributions using an adjusted holonomic gradient method,
24: <a href="https://doi.org/10.1007/s11222-017-9765-3"> doi </a> (2018)
1.24 takayama 25: <li> Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama, Nobuki Takayama,
26: Holonomic Gradient Method for Two Way Contingency Tables,
1.25 takayama 27: <a href="https://arxiv.org/abs/1803.04170"> arxiv:1803.04170 </a>
28: <li> F.H.Danufane, K.Ohara, N.Takayama, C.Siriteanu,
29: Holonomic Gradient Method-Based CDF Evaluation for the Largest Eigenvalue of a Complex Noncentral Wishart Matrix
30: (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 31: <a href="https://arxiv.org/abs/1707.02564"> arxiv:1707.02564 </a>
32: <li> T.Koyama,
33: An integral formula for the powered sum of the independent, identically and normally distributed random variables,
34: <a href="https://arxiv.org/abs/1706.03989"> arxiv:1706.03989 </a>
1.21 takayama 35: <li> H.Hashiguchi, N.Takayama, A.Takemura,
36: Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability
37: by Holonomic Gradient Method,
38: <a href="https://arxiv.org/abs/1610.09187"> arxiv:1610.09187 </a>
39:
1.18 takayama 40: <li> R.Vidunas, A.Takemura,
41: Differential relations for the largest root distribution
42: of complex non-central Wishart matrices,
43: <a href="http://arxiv.org/abs/1609.01799"> arxiv:1609.01799 </a>
44:
1.20 takayama 45: <li> S.Mano,
46: The A-hypergeometric System Associated with the Rational Normal Curve and
47: Exchangeable Structures,
48: <a href="http://arxiv.org/abs/1607.03569"> arxiv:1607.03569 </a>
49:
1.19 takayama 50: <li> M.Noro,
51: System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions,
52: <a href="http://dl.acm.org/citation.cfm?doid=2930889.2930905"> ACM DL </a>
53:
1.12 takayama 54: <li> Y.Goto, K.Matsumoto,
55: Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications,
1.13 takayama 56: <a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637 </a>
57:
58: <li> T.Koyama,
59: Holonomic gradient method for the probability content of a simplex
60: region
61: with a multivariate normal distribution,
62: <a href="http://arxiv.org/abs/1512.06564"> arxiv:1512.06564 </a>
63:
64:
65: <li> N.Takayama, S.Kuriki, A.Takemura,
66: A-Hpergeometric Distributions and Newton Polytopes,
67: <a href="http://arxiv.org/abs/1510.02269"> arxiv:1510.02269 </a>
68:
69: <li> G.Weyenberg, R.Yoshida, D.Howe,
70: Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace,
71: <a href="http://arxiv.org/abs/1506.00142"> arxiv:1506.00142 </a>
72:
1.17 takayama 73: <li> C.Siriteanu, A.Takemura, C.Koutschan, S.Kuriki, D.St.P.Richards, H.Sin,
74: Exact ZF Analysis and Computer-Algebra-Aided Evaluation
75: in Rank-1 LoS Rician Fading,
76: <a href="http://arxiv.org/abs/1507.07056"> arxiv:1507.07056 </a>
77:
1.13 takayama 78: <li> K.Ohara, N.Takayama,
79: Pfaffian Systems of A-Hypergeometric Systems II ---
80: Holonomic Gradient Method,
81: <a href="http://arxiv.org/abs/1505.02947"> arxiv:1505.02947 </a>
82:
83: <li> T.Koyama,
84: The Annihilating Ideal of the Fisher Integral,
85: <a href="http://arxiv.org/abs/1503.05261"> arxiv:1503.05261 </a>
86:
87: <li> T.Koyama, A.Takemura,
88: Holonomic gradient method for distribution function of a weighted sum
89: of noncentral chi-square random variables,
90: <a href="http://arxiv.org/abs/1503.00378"> arxiv:1503.00378 </a>
91:
92: <li> Y.Goto,
93: Contiguity relations of Lauricella's F_D revisited,
94: <a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a>
1.12 takayama 95:
1.15 takayama 96: <li>
97: T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama,
98: Software Packages for Holonomic Gradient Method,
99: Mathematial Software --- ICMS 2014,
100: 4th International Conference, Proceedings.
101: Edited by Hoon Hong and Chee Yap,
102: Springer lecture notes in computer science 8592,
103: 706--712.
104: <a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_105">
105: DOI
106: </a>
107:
1.11 takayama 108: <li>N.Marumo, T.Oaku, A.Takemura,
109: Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
110: <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
111:
1.8 takayama 112: <li> J.Hayakawa, A.Takemura,
113: Estimation of exponential-polynomial distribution by holonomic gradient descent
114: <a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
115:
116: <li> C.Siriteanu, A.Takemura, S.Kuriki,
117: MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
118: <a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
119:
1.4 takayama 120: <li> T.Koyama,
1.1 takayama 121: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
122: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
123:
124: <li> T.Hibi, K.Nishiyama, N.Takayama,
125: Pfaffian Systems of A-Hypergeometric Equations I,
126: Bases of Twisted Cohomology Groups,
127: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
1.22 takayama 128: (major revision v2 of arxiv:1212.6103).
129: Accepted version is at
130: <a href="http://dx.doi.org/10.1016/j.aim.2016.10.021"> DOI </a>
1.1 takayama 131:
132: <li> <img src="./wakaba01.png" alt="Intro">
133: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
134: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
135:
136: <li> <img src="./wakaba01.png" alt="Intro">
137: Introduction to the Holonomic Gradient Method (movie), 2013.
138: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
139:
1.2 takayama 140:
1.1 takayama 141: <li> T.Sei, A.Kume,
1.2 takayama 142: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1 takayama 143: Statistics and Computing, 2013,
144: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
145:
1.4 takayama 146: <li> T.Koyama, A.Takemura,
1.2 takayama 147: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
148: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
149:
1.1 takayama 150: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
151: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
152: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
1.11 takayama 153: Journal of Pure and Applied Algebra (online),
154: <a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
1.1 takayama 155:
156: <li>
157: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
158: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
159: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
160: Computational Statistics (2013)
161: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
162:
163: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
164: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
165: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
166: Journal of Multivariate Analysis, 117, (2013) 296-312,
167: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
168:
169: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
170: Properties and applications of Fisher distribution on the rotation group,
171: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
172: Journal of Multivariate Analysis, 116 (2013), 440--455,
173: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
174:
175: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
176: Funkcialaj Ekvacioj 56 (2013), 51--61.
1.11 takayama 177: <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
178: <!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
1.1 takayama 179:
180: <li>
181: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
182: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
183: Holonomic Gradient Descent and its Application to Fisher-Bingham Integral,
184: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> -->
185: Advances in Applied Mathematics 47 (2011), 639--658,
186: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
1.13 takayama 187:
1.1 takayama 188: </ol>
189:
1.13 takayama 190: Early papers related to HGM. <br>
191: <ol>
192: <li>
193: H.Dwinwoodie, L.Matusevich, E. Mosteig,
194: Transform methods for the hypergeometric distribution,
195: Statistics and Computing 14 (2004), 287--297.
196: </ol>
197:
198:
199:
1.2 takayama 200: <h2> Three Steps of HGM </h2>
201: <ol>
1.10 takayama 202: <li> Finding a holonomic system satisfied by the normalizing constant.
1.2 takayama 203: We may use computational or theoretical methods to find it.
204: Groebner basis and related methods are used.
1.10 takayama 205: <li> Finding an initial value vector for the holonomic system.
1.2 takayama 206: This is equivalent to evaluating the normalizing constant and its derivatives
207: at a point.
208: This step is usually performed by a series expansion.
1.10 takayama 209: <li> Solving the holonomic system numerically. We use several methods
1.2 takayama 210: in numerical analysis such as the Runge-Kutta method of solving
211: ordinary differential equations and efficient solvers of systems of linear
212: equations.
213: </ol>
214:
1.1 takayama 215: <h2> Software Packages for HGM</h2>
1.14 takayama 216:
1.15 takayama 217: <ul>
218: <li>
1.16 takayama 219: CRAN package <a href="https://cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).
1.14 takayama 220:
1.15 takayama 221: <li>
1.14 takayama 222: Some software packages are experimental and temporary documents are found in
1.6 takayama 223: "asir-contrib manual" (auto-autogenerated part), or
224: "Experimental Functions in Asir", or "miscellaneous and other documents"
225: of the
226: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7 takayama 227: OpenXM documents</a>
1.8 takayama 228: or in <a href="./"> this folder</a>.
1.10 takayama 229: The nightly snapshot of the asir-contrib can be found in the asir page below,
1.6 takayama 230: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8 takayama 231: cvsweb page</a>.
1.1 takayama 232: <ol>
1.9 takayama 233: <li> Command line interfaces are in the folder OpenXM/src/hgm
234: in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
235: OpenXM distribution page </a>.
1.14 takayama 236: <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 237: To install this package in R, type in
238: <pre>
239: R CMD install hgm_*.tar.gz
240: </pre>
1.10 takayama 241: <li> The following packages are
242: for the computer algebra system
243: <a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
244: They are in the asir-contrib collection.
245: <ul>
246: <li> yang.rr (for Pfaffian systems) ,
247: nk_restriction.rr (for D-module integrations),
248: tk_jack.rr (for Jack polynomials),
249: ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
250: are for the steps 1 or 2.
251: <li> nk_fb_gen_c.rr is a package to generate a C program to perform
1.7 takayama 252: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.10 takayama 253: <li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
254: </ul>
1.1 takayama 255: </ol>
256:
1.15 takayama 257: </ul>
258:
1.1 takayama 259: <h2> Programs to try examples of our papers </h2>
260: <ol>
261: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
262: </ol>
263:
1.27 ! takayama 264: <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.26 2018/07/06 06:01:51 takayama Exp $ </pre>
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