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