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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>
1.30 takayama 17: <li> M.Adamer, A.Lorincz, A.L.Sattelberger, B.Sturmfels, Algebraic Analysis of Rotation Data
18: <a href="https://arxiv.org/abs/1912.00396"> arxiv: 1912.00396 </a>
1.28 takayama 19: <li>
1.29 takayama 20: Anna-Laura Sattelberger, Bernd Sturmfels,
21: D-Modules and Holonomic Functions
22: <a href="https://arxiv.org/abs/1910.01395"> arxiv:1910.01395 </a>
23: <li>
1.28 takayama 24: N.Takayama, L.Jiu, S.Kuriki, Y.Zhang,
25: Computations of the Expected Euler Characteristic for the Largest Eigenvalue of a Real Wishart Matrix,
1.31 takayama 26: <!--
27: <a href="https://arxiv.org/abs/1903.10099"> arxiv:1903.10099 </a> -->
28: <a href="https://doi.org/10.1016/j.jmva.2020.104642"> jmva </a>
1.27 takayama 29: <li> M.Harkonen, T.Sei, Y.Hirose,
30: Holonomic extended least angle regression,
31: <a href="https://arxiv.org/abs/1809.08190"> arxiv:1809.08190 </a>
32: <li> S.Mano,
33: Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics,
34: <a href="https://www.springer.com/jp/book/9784431558866">
35: JSS Research Series in Statistics</a>, 2018.
1.26 takayama 36: <li> A.Kume, T.Sei,
37: On the exact maximum likelihood inference of Fisher–Bingham distributions using an adjusted holonomic gradient method,
38: <a href="https://doi.org/10.1007/s11222-017-9765-3"> doi </a> (2018)
1.24 takayama 39: <li> Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama, Nobuki Takayama,
40: Holonomic Gradient Method for Two Way Contingency Tables,
1.25 takayama 41: <a href="https://arxiv.org/abs/1803.04170"> arxiv:1803.04170 </a>
42: <li> F.H.Danufane, K.Ohara, N.Takayama, C.Siriteanu,
43: Holonomic Gradient Method-Based CDF Evaluation for the Largest Eigenvalue of a Complex Noncentral Wishart Matrix
44: (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 45: <a href="https://arxiv.org/abs/1707.02564"> arxiv:1707.02564 </a>
46: <li> T.Koyama,
47: An integral formula for the powered sum of the independent, identically and normally distributed random variables,
48: <a href="https://arxiv.org/abs/1706.03989"> arxiv:1706.03989 </a>
1.21 takayama 49: <li> H.Hashiguchi, N.Takayama, A.Takemura,
50: Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability
51: by Holonomic Gradient Method,
52: <a href="https://arxiv.org/abs/1610.09187"> arxiv:1610.09187 </a>
53:
1.18 takayama 54: <li> R.Vidunas, A.Takemura,
55: Differential relations for the largest root distribution
56: of complex non-central Wishart matrices,
57: <a href="http://arxiv.org/abs/1609.01799"> arxiv:1609.01799 </a>
58:
1.20 takayama 59: <li> S.Mano,
60: The A-hypergeometric System Associated with the Rational Normal Curve and
61: Exchangeable Structures,
62: <a href="http://arxiv.org/abs/1607.03569"> arxiv:1607.03569 </a>
63:
1.19 takayama 64: <li> M.Noro,
65: System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions,
66: <a href="http://dl.acm.org/citation.cfm?doid=2930889.2930905"> ACM DL </a>
67:
1.12 takayama 68: <li> Y.Goto, K.Matsumoto,
69: Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications,
1.13 takayama 70: <a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637 </a>
71:
72: <li> T.Koyama,
73: Holonomic gradient method for the probability content of a simplex
74: region
75: with a multivariate normal distribution,
76: <a href="http://arxiv.org/abs/1512.06564"> arxiv:1512.06564 </a>
77:
1.32 ! takayama 78: <li> N.Takayama, Holonomic Gradient Method (in Japanese, survey),
! 79: <a href="http://www.math.kobe-u.ac.jp/HOME/taka/2015/hgm-dic.pdf">
! 80: hgm-dic.pdf </a>
1.13 takayama 81:
82: <li> N.Takayama, S.Kuriki, A.Takemura,
83: A-Hpergeometric Distributions and Newton Polytopes,
84: <a href="http://arxiv.org/abs/1510.02269"> arxiv:1510.02269 </a>
85:
86: <li> G.Weyenberg, R.Yoshida, D.Howe,
87: Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace,
88: <a href="http://arxiv.org/abs/1506.00142"> arxiv:1506.00142 </a>
89:
1.17 takayama 90: <li> C.Siriteanu, A.Takemura, C.Koutschan, S.Kuriki, D.St.P.Richards, H.Sin,
91: Exact ZF Analysis and Computer-Algebra-Aided Evaluation
92: in Rank-1 LoS Rician Fading,
93: <a href="http://arxiv.org/abs/1507.07056"> arxiv:1507.07056 </a>
94:
1.13 takayama 95: <li> K.Ohara, N.Takayama,
96: Pfaffian Systems of A-Hypergeometric Systems II ---
97: Holonomic Gradient Method,
98: <a href="http://arxiv.org/abs/1505.02947"> arxiv:1505.02947 </a>
99:
100: <li> T.Koyama,
101: The Annihilating Ideal of the Fisher Integral,
102: <a href="http://arxiv.org/abs/1503.05261"> arxiv:1503.05261 </a>
103:
104: <li> T.Koyama, A.Takemura,
105: Holonomic gradient method for distribution function of a weighted sum
106: of noncentral chi-square random variables,
107: <a href="http://arxiv.org/abs/1503.00378"> arxiv:1503.00378 </a>
108:
109: <li> Y.Goto,
110: Contiguity relations of Lauricella's F_D revisited,
111: <a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a>
1.12 takayama 112:
1.15 takayama 113: <li>
114: T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama,
115: Software Packages for Holonomic Gradient Method,
116: Mathematial Software --- ICMS 2014,
117: 4th International Conference, Proceedings.
118: Edited by Hoon Hong and Chee Yap,
119: Springer lecture notes in computer science 8592,
120: 706--712.
121: <a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_105">
122: DOI
123: </a>
124:
1.11 takayama 125: <li>N.Marumo, T.Oaku, A.Takemura,
126: Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
127: <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
128:
1.8 takayama 129: <li> J.Hayakawa, A.Takemura,
130: Estimation of exponential-polynomial distribution by holonomic gradient descent
131: <a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
132:
133: <li> C.Siriteanu, A.Takemura, S.Kuriki,
134: MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
135: <a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
136:
1.4 takayama 137: <li> T.Koyama,
1.1 takayama 138: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
139: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
140:
141: <li> T.Hibi, K.Nishiyama, N.Takayama,
142: Pfaffian Systems of A-Hypergeometric Equations I,
143: Bases of Twisted Cohomology Groups,
144: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
1.22 takayama 145: (major revision v2 of arxiv:1212.6103).
146: Accepted version is at
147: <a href="http://dx.doi.org/10.1016/j.aim.2016.10.021"> DOI </a>
1.1 takayama 148:
149: <li> <img src="./wakaba01.png" alt="Intro">
150: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
151: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
152:
153: <li> <img src="./wakaba01.png" alt="Intro">
154: Introduction to the Holonomic Gradient Method (movie), 2013.
155: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
156:
1.2 takayama 157:
1.1 takayama 158: <li> T.Sei, A.Kume,
1.2 takayama 159: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1 takayama 160: Statistics and Computing, 2013,
161: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
162:
1.4 takayama 163: <li> T.Koyama, A.Takemura,
1.2 takayama 164: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
165: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
166:
1.1 takayama 167: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
168: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
169: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
1.11 takayama 170: Journal of Pure and Applied Algebra (online),
171: <a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
1.1 takayama 172:
173: <li>
174: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
175: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
176: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
177: Computational Statistics (2013)
178: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
179:
180: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
181: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
182: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
183: Journal of Multivariate Analysis, 117, (2013) 296-312,
184: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
185:
186: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
187: Properties and applications of Fisher distribution on the rotation group,
188: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
189: Journal of Multivariate Analysis, 116 (2013), 440--455,
190: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
191:
192: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
193: Funkcialaj Ekvacioj 56 (2013), 51--61.
1.11 takayama 194: <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
195: <!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
1.1 takayama 196:
197: <li>
198: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
199: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
200: Holonomic Gradient Descent and its Application to Fisher-Bingham Integral,
201: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> -->
202: Advances in Applied Mathematics 47 (2011), 639--658,
203: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
1.13 takayama 204:
1.1 takayama 205: </ol>
206:
1.13 takayama 207: Early papers related to HGM. <br>
208: <ol>
209: <li>
210: H.Dwinwoodie, L.Matusevich, E. Mosteig,
211: Transform methods for the hypergeometric distribution,
212: Statistics and Computing 14 (2004), 287--297.
213: </ol>
214:
215:
216:
1.2 takayama 217: <h2> Three Steps of HGM </h2>
218: <ol>
1.10 takayama 219: <li> Finding a holonomic system satisfied by the normalizing constant.
1.2 takayama 220: We may use computational or theoretical methods to find it.
221: Groebner basis and related methods are used.
1.10 takayama 222: <li> Finding an initial value vector for the holonomic system.
1.2 takayama 223: This is equivalent to evaluating the normalizing constant and its derivatives
224: at a point.
225: This step is usually performed by a series expansion.
1.10 takayama 226: <li> Solving the holonomic system numerically. We use several methods
1.2 takayama 227: in numerical analysis such as the Runge-Kutta method of solving
228: ordinary differential equations and efficient solvers of systems of linear
229: equations.
230: </ol>
231:
1.1 takayama 232: <h2> Software Packages for HGM</h2>
1.14 takayama 233:
1.15 takayama 234: <ul>
235: <li>
1.16 takayama 236: CRAN package <a href="https://cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).
1.14 takayama 237:
1.15 takayama 238: <li>
1.14 takayama 239: Some software packages are experimental and temporary documents are found in
1.6 takayama 240: "asir-contrib manual" (auto-autogenerated part), or
241: "Experimental Functions in Asir", or "miscellaneous and other documents"
242: of the
243: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7 takayama 244: OpenXM documents</a>
1.8 takayama 245: or in <a href="./"> this folder</a>.
1.10 takayama 246: The nightly snapshot of the asir-contrib can be found in the asir page below,
1.6 takayama 247: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8 takayama 248: cvsweb page</a>.
1.1 takayama 249: <ol>
1.9 takayama 250: <li> Command line interfaces are in the folder OpenXM/src/hgm
251: in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
252: OpenXM distribution page </a>.
1.14 takayama 253: <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 254: To install this package in R, type in
255: <pre>
256: R CMD install hgm_*.tar.gz
257: </pre>
1.10 takayama 258: <li> The following packages are
259: for the computer algebra system
260: <a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
261: They are in the asir-contrib collection.
262: <ul>
263: <li> yang.rr (for Pfaffian systems) ,
264: nk_restriction.rr (for D-module integrations),
265: tk_jack.rr (for Jack polynomials),
266: ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
267: are for the steps 1 or 2.
268: <li> nk_fb_gen_c.rr is a package to generate a C program to perform
1.7 takayama 269: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.10 takayama 270: <li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
271: </ul>
1.1 takayama 272: </ol>
273:
1.15 takayama 274: </ul>
275:
1.1 takayama 276: <h2> Programs to try examples of our papers </h2>
277: <ol>
278: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
279: </ol>
280:
1.32 ! takayama 281: <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.31 2020/06/11 22:39:10 takayama Exp $ </pre>
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