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10: <body>
11:
12: <h1> References for the Holonomic Gradient Method (HGM) and
13: the Holonomic Gradient Descent Method (HGD) </h1>
14:
15: <h2> Papers and Tutorials</h2>
16: <ol>
1.33 ! takayama 17: <li> Nobuki Takayama, Takaharu Yaguchi, Yi Zhang,
! 18: Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics,
! 19: <a href="https://arxiv.org/abs/2111.10947"> arxiv:2111.10947 </a>
! 20:
! 21: <li> Shuhei Mano, Nobuki Takayama,
! 22: Algebraic algorithm for direct sampling from toric models,
! 23: <a href="https://arxiv.org/abs/2110.14992"> arxiv:2110.14992 </a>
! 24:
1.30 takayama 25: <li> M.Adamer, A.Lorincz, A.L.Sattelberger, B.Sturmfels, Algebraic Analysis of Rotation Data
26: <a href="https://arxiv.org/abs/1912.00396"> arxiv: 1912.00396 </a>
1.28 takayama 27: <li>
1.29 takayama 28: Anna-Laura Sattelberger, Bernd Sturmfels,
29: D-Modules and Holonomic Functions
30: <a href="https://arxiv.org/abs/1910.01395"> arxiv:1910.01395 </a>
31: <li>
1.28 takayama 32: N.Takayama, L.Jiu, S.Kuriki, Y.Zhang,
33: Computations of the Expected Euler Characteristic for the Largest Eigenvalue of a Real Wishart Matrix,
1.31 takayama 34: <!--
35: <a href="https://arxiv.org/abs/1903.10099"> arxiv:1903.10099 </a> -->
36: <a href="https://doi.org/10.1016/j.jmva.2020.104642"> jmva </a>
1.27 takayama 37: <li> M.Harkonen, T.Sei, Y.Hirose,
38: Holonomic extended least angle regression,
39: <a href="https://arxiv.org/abs/1809.08190"> arxiv:1809.08190 </a>
40: <li> S.Mano,
41: Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics,
42: <a href="https://www.springer.com/jp/book/9784431558866">
43: JSS Research Series in Statistics</a>, 2018.
1.26 takayama 44: <li> A.Kume, T.Sei,
45: On the exact maximum likelihood inference of Fisher–Bingham distributions using an adjusted holonomic gradient method,
46: <a href="https://doi.org/10.1007/s11222-017-9765-3"> doi </a> (2018)
1.24 takayama 47: <li> Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama, Nobuki Takayama,
48: Holonomic Gradient Method for Two Way Contingency Tables,
1.25 takayama 49: <a href="https://arxiv.org/abs/1803.04170"> arxiv:1803.04170 </a>
50: <li> F.H.Danufane, K.Ohara, N.Takayama, C.Siriteanu,
51: Holonomic Gradient Method-Based CDF Evaluation for the Largest Eigenvalue of a Complex Noncentral Wishart Matrix
52: (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 53: <a href="https://arxiv.org/abs/1707.02564"> arxiv:1707.02564 </a>
54: <li> T.Koyama,
55: An integral formula for the powered sum of the independent, identically and normally distributed random variables,
56: <a href="https://arxiv.org/abs/1706.03989"> arxiv:1706.03989 </a>
1.21 takayama 57: <li> H.Hashiguchi, N.Takayama, A.Takemura,
58: Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability
59: by Holonomic Gradient Method,
60: <a href="https://arxiv.org/abs/1610.09187"> arxiv:1610.09187 </a>
61:
1.18 takayama 62: <li> R.Vidunas, A.Takemura,
63: Differential relations for the largest root distribution
64: of complex non-central Wishart matrices,
65: <a href="http://arxiv.org/abs/1609.01799"> arxiv:1609.01799 </a>
66:
1.20 takayama 67: <li> S.Mano,
68: The A-hypergeometric System Associated with the Rational Normal Curve and
69: Exchangeable Structures,
70: <a href="http://arxiv.org/abs/1607.03569"> arxiv:1607.03569 </a>
71:
1.19 takayama 72: <li> M.Noro,
73: System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions,
74: <a href="http://dl.acm.org/citation.cfm?doid=2930889.2930905"> ACM DL </a>
75:
1.12 takayama 76: <li> Y.Goto, K.Matsumoto,
77: Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications,
1.13 takayama 78: <a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637 </a>
79:
80: <li> T.Koyama,
81: Holonomic gradient method for the probability content of a simplex
82: region
83: with a multivariate normal distribution,
84: <a href="http://arxiv.org/abs/1512.06564"> arxiv:1512.06564 </a>
85:
1.32 takayama 86: <li> N.Takayama, Holonomic Gradient Method (in Japanese, survey),
87: <a href="http://www.math.kobe-u.ac.jp/HOME/taka/2015/hgm-dic.pdf">
88: hgm-dic.pdf </a>
1.13 takayama 89:
90: <li> N.Takayama, S.Kuriki, A.Takemura,
91: A-Hpergeometric Distributions and Newton Polytopes,
92: <a href="http://arxiv.org/abs/1510.02269"> arxiv:1510.02269 </a>
93:
94: <li> G.Weyenberg, R.Yoshida, D.Howe,
95: Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace,
96: <a href="http://arxiv.org/abs/1506.00142"> arxiv:1506.00142 </a>
97:
1.17 takayama 98: <li> C.Siriteanu, A.Takemura, C.Koutschan, S.Kuriki, D.St.P.Richards, H.Sin,
99: Exact ZF Analysis and Computer-Algebra-Aided Evaluation
100: in Rank-1 LoS Rician Fading,
101: <a href="http://arxiv.org/abs/1507.07056"> arxiv:1507.07056 </a>
102:
1.13 takayama 103: <li> K.Ohara, N.Takayama,
104: Pfaffian Systems of A-Hypergeometric Systems II ---
105: Holonomic Gradient Method,
106: <a href="http://arxiv.org/abs/1505.02947"> arxiv:1505.02947 </a>
107:
108: <li> T.Koyama,
109: The Annihilating Ideal of the Fisher Integral,
110: <a href="http://arxiv.org/abs/1503.05261"> arxiv:1503.05261 </a>
111:
112: <li> T.Koyama, A.Takemura,
113: Holonomic gradient method for distribution function of a weighted sum
114: of noncentral chi-square random variables,
115: <a href="http://arxiv.org/abs/1503.00378"> arxiv:1503.00378 </a>
116:
117: <li> Y.Goto,
118: Contiguity relations of Lauricella's F_D revisited,
119: <a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a>
1.12 takayama 120:
1.15 takayama 121: <li>
122: T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama,
123: Software Packages for Holonomic Gradient Method,
124: Mathematial Software --- ICMS 2014,
125: 4th International Conference, Proceedings.
126: Edited by Hoon Hong and Chee Yap,
127: Springer lecture notes in computer science 8592,
128: 706--712.
129: <a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_105">
130: DOI
131: </a>
132:
1.11 takayama 133: <li>N.Marumo, T.Oaku, A.Takemura,
134: Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
135: <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
136:
1.8 takayama 137: <li> J.Hayakawa, A.Takemura,
138: Estimation of exponential-polynomial distribution by holonomic gradient descent
139: <a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
140:
141: <li> C.Siriteanu, A.Takemura, S.Kuriki,
142: MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
143: <a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
144:
1.4 takayama 145: <li> T.Koyama,
1.1 takayama 146: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
147: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
148:
149: <li> T.Hibi, K.Nishiyama, N.Takayama,
150: Pfaffian Systems of A-Hypergeometric Equations I,
151: Bases of Twisted Cohomology Groups,
152: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
1.22 takayama 153: (major revision v2 of arxiv:1212.6103).
154: Accepted version is at
155: <a href="http://dx.doi.org/10.1016/j.aim.2016.10.021"> DOI </a>
1.1 takayama 156:
157: <li> <img src="./wakaba01.png" alt="Intro">
158: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
159: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
160:
161: <li> <img src="./wakaba01.png" alt="Intro">
162: Introduction to the Holonomic Gradient Method (movie), 2013.
163: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
164:
1.2 takayama 165:
1.1 takayama 166: <li> T.Sei, A.Kume,
1.2 takayama 167: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1 takayama 168: Statistics and Computing, 2013,
169: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
170:
1.4 takayama 171: <li> T.Koyama, A.Takemura,
1.2 takayama 172: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
173: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
174:
1.1 takayama 175: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
176: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
177: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
1.11 takayama 178: Journal of Pure and Applied Algebra (online),
179: <a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
1.1 takayama 180:
181: <li>
182: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
183: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
184: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
185: Computational Statistics (2013)
186: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
187:
188: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
189: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
190: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
191: Journal of Multivariate Analysis, 117, (2013) 296-312,
192: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
193:
194: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
195: Properties and applications of Fisher distribution on the rotation group,
196: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
197: Journal of Multivariate Analysis, 116 (2013), 440--455,
198: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
199:
200: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
201: Funkcialaj Ekvacioj 56 (2013), 51--61.
1.11 takayama 202: <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
203: <!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
1.1 takayama 204:
205: <li>
206: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
207: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
208: Holonomic Gradient Descent and its Application to Fisher-Bingham Integral,
209: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> -->
210: Advances in Applied Mathematics 47 (2011), 639--658,
211: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
1.13 takayama 212:
1.1 takayama 213: </ol>
214:
1.13 takayama 215: Early papers related to HGM. <br>
216: <ol>
217: <li>
218: H.Dwinwoodie, L.Matusevich, E. Mosteig,
219: Transform methods for the hypergeometric distribution,
220: Statistics and Computing 14 (2004), 287--297.
221: </ol>
222:
223:
224:
1.2 takayama 225: <h2> Three Steps of HGM </h2>
226: <ol>
1.10 takayama 227: <li> Finding a holonomic system satisfied by the normalizing constant.
1.2 takayama 228: We may use computational or theoretical methods to find it.
229: Groebner basis and related methods are used.
1.10 takayama 230: <li> Finding an initial value vector for the holonomic system.
1.2 takayama 231: This is equivalent to evaluating the normalizing constant and its derivatives
232: at a point.
233: This step is usually performed by a series expansion.
1.10 takayama 234: <li> Solving the holonomic system numerically. We use several methods
1.2 takayama 235: in numerical analysis such as the Runge-Kutta method of solving
236: ordinary differential equations and efficient solvers of systems of linear
237: equations.
238: </ol>
239:
1.1 takayama 240: <h2> Software Packages for HGM</h2>
1.14 takayama 241:
1.15 takayama 242: <ul>
243: <li>
1.16 takayama 244: CRAN package <a href="https://cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).
1.14 takayama 245:
1.15 takayama 246: <li>
1.14 takayama 247: Some software packages are experimental and temporary documents are found in
1.6 takayama 248: "asir-contrib manual" (auto-autogenerated part), or
249: "Experimental Functions in Asir", or "miscellaneous and other documents"
250: of the
251: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7 takayama 252: OpenXM documents</a>
1.8 takayama 253: or in <a href="./"> this folder</a>.
1.10 takayama 254: The nightly snapshot of the asir-contrib can be found in the asir page below,
1.6 takayama 255: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8 takayama 256: cvsweb page</a>.
1.1 takayama 257: <ol>
1.9 takayama 258: <li> Command line interfaces are in the folder OpenXM/src/hgm
259: in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
260: OpenXM distribution page </a>.
1.14 takayama 261: <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 262: To install this package in R, type in
263: <pre>
264: R CMD install hgm_*.tar.gz
265: </pre>
1.10 takayama 266: <li> The following packages are
267: for the computer algebra system
268: <a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
269: They are in the asir-contrib collection.
270: <ul>
271: <li> yang.rr (for Pfaffian systems) ,
272: nk_restriction.rr (for D-module integrations),
273: tk_jack.rr (for Jack polynomials),
274: ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
275: are for the steps 1 or 2.
276: <li> nk_fb_gen_c.rr is a package to generate a C program to perform
1.7 takayama 277: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.10 takayama 278: <li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
279: </ul>
1.1 takayama 280: </ol>
281:
1.15 takayama 282: </ul>
283:
1.1 takayama 284: <h2> Programs to try examples of our papers </h2>
285: <ol>
286: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
287: </ol>
288:
1.33 ! takayama 289: <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.32 2020/08/24 23:24:27 takayama Exp $ </pre>
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