Annotation of OpenXM/src/hgm/doc/ref-hgm.html, Revision 1.30
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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,
26: <a href="https://arxiv.org/abs/1903.10099"> arxiv:1903.10099 </a>
1.27 takayama 27: <li> M.Harkonen, T.Sei, Y.Hirose,
28: Holonomic extended least angle regression,
29: <a href="https://arxiv.org/abs/1809.08190"> arxiv:1809.08190 </a>
30: <li> S.Mano,
31: Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics,
32: <a href="https://www.springer.com/jp/book/9784431558866">
33: JSS Research Series in Statistics</a>, 2018.
1.26 takayama 34: <li> A.Kume, T.Sei,
35: On the exact maximum likelihood inference of Fisher–Bingham distributions using an adjusted holonomic gradient method,
36: <a href="https://doi.org/10.1007/s11222-017-9765-3"> doi </a> (2018)
1.24 takayama 37: <li> Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama, Nobuki Takayama,
38: Holonomic Gradient Method for Two Way Contingency Tables,
1.25 takayama 39: <a href="https://arxiv.org/abs/1803.04170"> arxiv:1803.04170 </a>
40: <li> F.H.Danufane, K.Ohara, N.Takayama, C.Siriteanu,
41: Holonomic Gradient Method-Based CDF Evaluation for the Largest Eigenvalue of a Complex Noncentral Wishart Matrix
42: (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 43: <a href="https://arxiv.org/abs/1707.02564"> arxiv:1707.02564 </a>
44: <li> T.Koyama,
45: An integral formula for the powered sum of the independent, identically and normally distributed random variables,
46: <a href="https://arxiv.org/abs/1706.03989"> arxiv:1706.03989 </a>
1.21 takayama 47: <li> H.Hashiguchi, N.Takayama, A.Takemura,
48: Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability
49: by Holonomic Gradient Method,
50: <a href="https://arxiv.org/abs/1610.09187"> arxiv:1610.09187 </a>
51:
1.18 takayama 52: <li> R.Vidunas, A.Takemura,
53: Differential relations for the largest root distribution
54: of complex non-central Wishart matrices,
55: <a href="http://arxiv.org/abs/1609.01799"> arxiv:1609.01799 </a>
56:
1.20 takayama 57: <li> S.Mano,
58: The A-hypergeometric System Associated with the Rational Normal Curve and
59: Exchangeable Structures,
60: <a href="http://arxiv.org/abs/1607.03569"> arxiv:1607.03569 </a>
61:
1.19 takayama 62: <li> M.Noro,
63: System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions,
64: <a href="http://dl.acm.org/citation.cfm?doid=2930889.2930905"> ACM DL </a>
65:
1.12 takayama 66: <li> Y.Goto, K.Matsumoto,
67: Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications,
1.13 takayama 68: <a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637 </a>
69:
70: <li> T.Koyama,
71: Holonomic gradient method for the probability content of a simplex
72: region
73: with a multivariate normal distribution,
74: <a href="http://arxiv.org/abs/1512.06564"> arxiv:1512.06564 </a>
75:
76:
77: <li> N.Takayama, S.Kuriki, A.Takemura,
78: A-Hpergeometric Distributions and Newton Polytopes,
79: <a href="http://arxiv.org/abs/1510.02269"> arxiv:1510.02269 </a>
80:
81: <li> G.Weyenberg, R.Yoshida, D.Howe,
82: Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace,
83: <a href="http://arxiv.org/abs/1506.00142"> arxiv:1506.00142 </a>
84:
1.17 takayama 85: <li> C.Siriteanu, A.Takemura, C.Koutschan, S.Kuriki, D.St.P.Richards, H.Sin,
86: Exact ZF Analysis and Computer-Algebra-Aided Evaluation
87: in Rank-1 LoS Rician Fading,
88: <a href="http://arxiv.org/abs/1507.07056"> arxiv:1507.07056 </a>
89:
1.13 takayama 90: <li> K.Ohara, N.Takayama,
91: Pfaffian Systems of A-Hypergeometric Systems II ---
92: Holonomic Gradient Method,
93: <a href="http://arxiv.org/abs/1505.02947"> arxiv:1505.02947 </a>
94:
95: <li> T.Koyama,
96: The Annihilating Ideal of the Fisher Integral,
97: <a href="http://arxiv.org/abs/1503.05261"> arxiv:1503.05261 </a>
98:
99: <li> T.Koyama, A.Takemura,
100: Holonomic gradient method for distribution function of a weighted sum
101: of noncentral chi-square random variables,
102: <a href="http://arxiv.org/abs/1503.00378"> arxiv:1503.00378 </a>
103:
104: <li> Y.Goto,
105: Contiguity relations of Lauricella's F_D revisited,
106: <a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a>
1.12 takayama 107:
1.15 takayama 108: <li>
109: T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama,
110: Software Packages for Holonomic Gradient Method,
111: Mathematial Software --- ICMS 2014,
112: 4th International Conference, Proceedings.
113: Edited by Hoon Hong and Chee Yap,
114: Springer lecture notes in computer science 8592,
115: 706--712.
116: <a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_105">
117: DOI
118: </a>
119:
1.11 takayama 120: <li>N.Marumo, T.Oaku, A.Takemura,
121: Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
122: <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
123:
1.8 takayama 124: <li> J.Hayakawa, A.Takemura,
125: Estimation of exponential-polynomial distribution by holonomic gradient descent
126: <a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
127:
128: <li> C.Siriteanu, A.Takemura, S.Kuriki,
129: MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
130: <a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
131:
1.4 takayama 132: <li> T.Koyama,
1.1 takayama 133: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
134: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
135:
136: <li> T.Hibi, K.Nishiyama, N.Takayama,
137: Pfaffian Systems of A-Hypergeometric Equations I,
138: Bases of Twisted Cohomology Groups,
139: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
1.22 takayama 140: (major revision v2 of arxiv:1212.6103).
141: Accepted version is at
142: <a href="http://dx.doi.org/10.1016/j.aim.2016.10.021"> DOI </a>
1.1 takayama 143:
144: <li> <img src="./wakaba01.png" alt="Intro">
145: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
146: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
147:
148: <li> <img src="./wakaba01.png" alt="Intro">
149: Introduction to the Holonomic Gradient Method (movie), 2013.
150: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
151:
1.2 takayama 152:
1.1 takayama 153: <li> T.Sei, A.Kume,
1.2 takayama 154: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1 takayama 155: Statistics and Computing, 2013,
156: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
157:
1.4 takayama 158: <li> T.Koyama, A.Takemura,
1.2 takayama 159: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
160: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
161:
1.1 takayama 162: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
163: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
164: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
1.11 takayama 165: Journal of Pure and Applied Algebra (online),
166: <a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
1.1 takayama 167:
168: <li>
169: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
170: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
171: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
172: Computational Statistics (2013)
173: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
174:
175: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
176: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
177: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
178: Journal of Multivariate Analysis, 117, (2013) 296-312,
179: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
180:
181: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
182: Properties and applications of Fisher distribution on the rotation group,
183: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
184: Journal of Multivariate Analysis, 116 (2013), 440--455,
185: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
186:
187: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
188: Funkcialaj Ekvacioj 56 (2013), 51--61.
1.11 takayama 189: <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
190: <!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
1.1 takayama 191:
192: <li>
193: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
194: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
195: Holonomic Gradient Descent and its Application to Fisher-Bingham Integral,
196: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> -->
197: Advances in Applied Mathematics 47 (2011), 639--658,
198: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
1.13 takayama 199:
1.1 takayama 200: </ol>
201:
1.13 takayama 202: Early papers related to HGM. <br>
203: <ol>
204: <li>
205: H.Dwinwoodie, L.Matusevich, E. Mosteig,
206: Transform methods for the hypergeometric distribution,
207: Statistics and Computing 14 (2004), 287--297.
208: </ol>
209:
210:
211:
1.2 takayama 212: <h2> Three Steps of HGM </h2>
213: <ol>
1.10 takayama 214: <li> Finding a holonomic system satisfied by the normalizing constant.
1.2 takayama 215: We may use computational or theoretical methods to find it.
216: Groebner basis and related methods are used.
1.10 takayama 217: <li> Finding an initial value vector for the holonomic system.
1.2 takayama 218: This is equivalent to evaluating the normalizing constant and its derivatives
219: at a point.
220: This step is usually performed by a series expansion.
1.10 takayama 221: <li> Solving the holonomic system numerically. We use several methods
1.2 takayama 222: in numerical analysis such as the Runge-Kutta method of solving
223: ordinary differential equations and efficient solvers of systems of linear
224: equations.
225: </ol>
226:
1.1 takayama 227: <h2> Software Packages for HGM</h2>
1.14 takayama 228:
1.15 takayama 229: <ul>
230: <li>
1.16 takayama 231: CRAN package <a href="https://cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).
1.14 takayama 232:
1.15 takayama 233: <li>
1.14 takayama 234: Some software packages are experimental and temporary documents are found in
1.6 takayama 235: "asir-contrib manual" (auto-autogenerated part), or
236: "Experimental Functions in Asir", or "miscellaneous and other documents"
237: of the
238: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7 takayama 239: OpenXM documents</a>
1.8 takayama 240: or in <a href="./"> this folder</a>.
1.10 takayama 241: The nightly snapshot of the asir-contrib can be found in the asir page below,
1.6 takayama 242: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8 takayama 243: cvsweb page</a>.
1.1 takayama 244: <ol>
1.9 takayama 245: <li> Command line interfaces are in the folder OpenXM/src/hgm
246: in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
247: OpenXM distribution page </a>.
1.14 takayama 248: <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 249: To install this package in R, type in
250: <pre>
251: R CMD install hgm_*.tar.gz
252: </pre>
1.10 takayama 253: <li> The following packages are
254: for the computer algebra system
255: <a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
256: They are in the asir-contrib collection.
257: <ul>
258: <li> yang.rr (for Pfaffian systems) ,
259: nk_restriction.rr (for D-module integrations),
260: tk_jack.rr (for Jack polynomials),
261: ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
262: are for the steps 1 or 2.
263: <li> nk_fb_gen_c.rr is a package to generate a C program to perform
1.7 takayama 264: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.10 takayama 265: <li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
266: </ul>
1.1 takayama 267: </ol>
268:
1.15 takayama 269: </ul>
270:
1.1 takayama 271: <h2> Programs to try examples of our papers </h2>
272: <ol>
273: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
274: </ol>
275:
1.30 ! takayama 276: <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.29 2019/10/31 01:53:51 takayama Exp $ </pre>
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