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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>
1.12 takayama 15: <li> Y.Goto, K.Matsumoto,
16: Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications,
1.13 ! takayama 17: <a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637 </a>
! 18:
! 19: <li> T.Koyama,
! 20: Holonomic gradient method for the probability content of a simplex
! 21: region
! 22: with a multivariate normal distribution,
! 23: <a href="http://arxiv.org/abs/1512.06564"> arxiv:1512.06564 </a>
! 24:
! 25:
! 26: <li> N.Takayama, S.Kuriki, A.Takemura,
! 27: A-Hpergeometric Distributions and Newton Polytopes,
! 28: <a href="http://arxiv.org/abs/1510.02269"> arxiv:1510.02269 </a>
! 29:
! 30: <li> G.Weyenberg, R.Yoshida, D.Howe,
! 31: Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace,
! 32: <a href="http://arxiv.org/abs/1506.00142"> arxiv:1506.00142 </a>
! 33:
! 34: <li> K.Ohara, N.Takayama,
! 35: Pfaffian Systems of A-Hypergeometric Systems II ---
! 36: Holonomic Gradient Method,
! 37: <a href="http://arxiv.org/abs/1505.02947"> arxiv:1505.02947 </a>
! 38:
! 39: <li> T.Koyama,
! 40: The Annihilating Ideal of the Fisher Integral,
! 41: <a href="http://arxiv.org/abs/1503.05261"> arxiv:1503.05261 </a>
! 42:
! 43: <li> T.Koyama, A.Takemura,
! 44: Holonomic gradient method for distribution function of a weighted sum
! 45: of noncentral chi-square random variables,
! 46: <a href="http://arxiv.org/abs/1503.00378"> arxiv:1503.00378 </a>
! 47:
! 48: <li> Y.Goto,
! 49: Contiguity relations of Lauricella's F_D revisited,
! 50: <a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a>
1.12 takayama 51:
1.11 takayama 52: <li>N.Marumo, T.Oaku, A.Takemura,
53: Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
54: <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
55:
1.8 takayama 56: <li> J.Hayakawa, A.Takemura,
57: Estimation of exponential-polynomial distribution by holonomic gradient descent
58: <a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
59:
60: <li> C.Siriteanu, A.Takemura, S.Kuriki,
61: MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
62: <a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
63:
1.4 takayama 64: <li> T.Koyama,
1.1 takayama 65: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
66: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
67:
68: <li> T.Hibi, K.Nishiyama, N.Takayama,
69: Pfaffian Systems of A-Hypergeometric Equations I,
70: Bases of Twisted Cohomology Groups,
71: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
72: (major revision v2 of arxiv:1212.6103)
73:
74: <li> <img src="./wakaba01.png" alt="Intro">
75: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
76: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
77:
78: <li> <img src="./wakaba01.png" alt="Intro">
79: Introduction to the Holonomic Gradient Method (movie), 2013.
80: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
81:
1.2 takayama 82:
1.1 takayama 83: <li> T.Sei, A.Kume,
1.2 takayama 84: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1 takayama 85: Statistics and Computing, 2013,
86: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
87:
1.4 takayama 88: <li> T.Koyama, A.Takemura,
1.2 takayama 89: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
90: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
91:
1.1 takayama 92: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
93: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
94: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
1.11 takayama 95: Journal of Pure and Applied Algebra (online),
96: <a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
1.1 takayama 97:
98: <li>
99: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
100: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
101: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
102: Computational Statistics (2013)
103: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
104:
105: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
106: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
107: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
108: Journal of Multivariate Analysis, 117, (2013) 296-312,
109: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
110:
111: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
112: Properties and applications of Fisher distribution on the rotation group,
113: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
114: Journal of Multivariate Analysis, 116 (2013), 440--455,
115: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
116:
117: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
118: Funkcialaj Ekvacioj 56 (2013), 51--61.
1.11 takayama 119: <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
120: <!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
1.1 takayama 121:
122: <li>
123: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
124: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
125: Holonomic Gradient Descent and its Application to Fisher-Bingham Integral,
126: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> -->
127: Advances in Applied Mathematics 47 (2011), 639--658,
128: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
1.13 ! takayama 129:
1.1 takayama 130: </ol>
131:
1.13 ! takayama 132: Early papers related to HGM. <br>
! 133: <ol>
! 134: <li>
! 135: H.Dwinwoodie, L.Matusevich, E. Mosteig,
! 136: Transform methods for the hypergeometric distribution,
! 137: Statistics and Computing 14 (2004), 287--297.
! 138: </ol>
! 139:
! 140:
! 141:
1.2 takayama 142: <h2> Three Steps of HGM </h2>
143: <ol>
1.10 takayama 144: <li> Finding a holonomic system satisfied by the normalizing constant.
1.2 takayama 145: We may use computational or theoretical methods to find it.
146: Groebner basis and related methods are used.
1.10 takayama 147: <li> Finding an initial value vector for the holonomic system.
1.2 takayama 148: This is equivalent to evaluating the normalizing constant and its derivatives
149: at a point.
150: This step is usually performed by a series expansion.
1.10 takayama 151: <li> Solving the holonomic system numerically. We use several methods
1.2 takayama 152: in numerical analysis such as the Runge-Kutta method of solving
153: ordinary differential equations and efficient solvers of systems of linear
154: equations.
155: </ol>
156:
1.1 takayama 157: <h2> Software Packages for HGM</h2>
1.6 takayama 158: Most software packages are experimental and temporary documents are found in
159: "asir-contrib manual" (auto-autogenerated part), or
160: "Experimental Functions in Asir", or "miscellaneous and other documents"
161: of the
162: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7 takayama 163: OpenXM documents</a>
1.8 takayama 164: or in <a href="./"> this folder</a>.
1.10 takayama 165: The nightly snapshot of the asir-contrib can be found in the asir page below,
1.6 takayama 166: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8 takayama 167: cvsweb page</a>.
1.1 takayama 168: <ol>
1.9 takayama 169: <li> Command line interfaces are in the folder OpenXM/src/hgm
170: in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
171: OpenXM distribution page </a>.
1.11 takayama 172: <li> <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.
173: To install this package in R, type in
174: <pre>
175: R CMD install hgm_*.tar.gz
176: </pre>
1.10 takayama 177: <li> The following packages are
178: for the computer algebra system
179: <a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
180: They are in the asir-contrib collection.
181: <ul>
182: <li> yang.rr (for Pfaffian systems) ,
183: nk_restriction.rr (for D-module integrations),
184: tk_jack.rr (for Jack polynomials),
185: ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
186: are for the steps 1 or 2.
187: <li> nk_fb_gen_c.rr is a package to generate a C program to perform
1.7 takayama 188: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.10 takayama 189: <li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
190: </ul>
1.1 takayama 191: </ol>
192:
193: <h2> Programs to try examples of our papers </h2>
194: <ol>
195: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
196: </ol>
197:
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