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                      5: <title>References for HGM</title> <!-- Use UTF-8 文字 code-->
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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>
1.21      takayama   15: <li> H.Hashiguchi, N.Takayama, A.Takemura,
                     16: Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability
                     17: by Holonomic Gradient Method,
                     18: <a href="https://arxiv.org/abs/1610.09187"> arxiv:1610.09187 </a>
                     19:
1.18      takayama   20: <li> R.Vidunas, A.Takemura,
                     21: Differential relations for the largest root distribution
                     22: of complex non-central Wishart matrices,
                     23: <a href="http://arxiv.org/abs/1609.01799"> arxiv:1609.01799 </a>
                     24:
1.20      takayama   25: <li> S.Mano,
                     26: The A-hypergeometric System Associated with the Rational Normal Curve and
                     27: Exchangeable Structures,
                     28: <a href="http://arxiv.org/abs/1607.03569"> arxiv:1607.03569 </a>
                     29:
1.19      takayama   30: <li> M.Noro,
                     31: System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions,
                     32: <a href="http://dl.acm.org/citation.cfm?doid=2930889.2930905"> ACM DL </a>
                     33:
1.12      takayama   34: <li> Y.Goto, K.Matsumoto,
                     35: Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications,
1.13      takayama   36: <a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637 </a>
                     37:
                     38: <li>  T.Koyama,
                     39: Holonomic gradient method for the probability content of a simplex
                     40: region
                     41: with a multivariate normal distribution,
                     42: <a href="http://arxiv.org/abs/1512.06564">  arxiv:1512.06564 </a>
                     43:
                     44:
                     45: <li> N.Takayama, S.Kuriki, A.Takemura,
                     46: A-Hpergeometric Distributions and Newton Polytopes,
                     47: <a href="http://arxiv.org/abs/1510.02269">  arxiv:1510.02269 </a>
                     48:
                     49: <li> G.Weyenberg, R.Yoshida, D.Howe,
                     50: Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace,
                     51: <a href="http://arxiv.org/abs/1506.00142"> arxiv:1506.00142 </a>
                     52:
1.17      takayama   53: <li> C.Siriteanu, A.Takemura, C.Koutschan, S.Kuriki, D.St.P.Richards, H.Sin,
                     54: Exact ZF Analysis and Computer-Algebra-Aided Evaluation
                     55: in Rank-1 LoS Rician Fading,
                     56: <a href="http://arxiv.org/abs/1507.07056"> arxiv:1507.07056 </a>
                     57:
1.13      takayama   58: <li> K.Ohara, N.Takayama,
                     59: Pfaffian Systems of A-Hypergeometric Systems II ---
                     60: Holonomic Gradient Method,
                     61: <a href="http://arxiv.org/abs/1505.02947"> arxiv:1505.02947 </a>
                     62:
                     63: <li> T.Koyama,
                     64: The Annihilating Ideal of the Fisher Integral,
                     65: <a href="http://arxiv.org/abs/1503.05261"> arxiv:1503.05261 </a>
                     66:
                     67: <li> T.Koyama, A.Takemura,
                     68: Holonomic gradient method for distribution function of a weighted sum
                     69: of noncentral chi-square random variables,
                     70: <a href="http://arxiv.org/abs/1503.00378"> arxiv:1503.00378 </a>
                     71:
                     72: <li> Y.Goto,
                     73: Contiguity relations of Lauricella's F_D revisited,
                     74: <a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a>
1.12      takayama   75:
1.15      takayama   76: <li>
                     77: T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama,
                     78: Software Packages for Holonomic Gradient Method,
                     79: Mathematial Software --- ICMS 2014,
                     80: 4th International Conference, Proceedings.
                     81: Edited by Hoon Hong and Chee Yap,
                     82: Springer lecture notes in computer science 8592,
                     83: 706--712.
                     84: <a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_105">
                     85: DOI
                     86: </a>
                     87:
1.11      takayama   88: <li>N.Marumo, T.Oaku, A.Takemura,
                     89: Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
                     90: <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
                     91:
1.8       takayama   92: <li> J.Hayakawa, A.Takemura,
                     93: Estimation of exponential-polynomial distribution by holonomic gradient descent
                     94: <a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
                     95:
                     96: <li> C.Siriteanu, A.Takemura, S.Kuriki,
                     97: MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
                     98: <a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
                     99:
1.4       takayama  100: <li> T.Koyama,
1.1       takayama  101: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
                    102: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
                    103:
                    104: <li> T.Hibi, K.Nishiyama, N.Takayama,
                    105: Pfaffian Systems of A-Hypergeometric Equations I,
                    106: Bases of Twisted Cohomology Groups,
                    107: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
1.22    ! takayama  108: (major revision v2 of arxiv:1212.6103).
        !           109: Accepted version is at
        !           110: <a href="http://dx.doi.org/10.1016/j.aim.2016.10.021"> DOI </a>
1.1       takayama  111:
                    112: <li> <img src="./wakaba01.png" alt="Intro">
                    113: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
                    114: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
                    115:
                    116: <li> <img src="./wakaba01.png" alt="Intro">
                    117: Introduction to the Holonomic Gradient Method (movie), 2013.
                    118: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
                    119:
1.2       takayama  120:
1.1       takayama  121: <li> T.Sei, A.Kume,
1.2       takayama  122: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1       takayama  123: Statistics and Computing, 2013,
                    124: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
                    125:
1.4       takayama  126: <li> T.Koyama, A.Takemura,
1.2       takayama  127: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
                    128: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
                    129:
1.1       takayama  130: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
                    131: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
                    132: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
1.11      takayama  133: Journal of Pure and Applied Algebra  (online),
                    134: <a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
1.1       takayama  135:
                    136: <li>
                    137: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
                    138: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
                    139: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
                    140: Computational Statistics (2013)
                    141: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
                    142:
                    143: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
                    144: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
                    145: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
                    146: Journal of Multivariate Analysis, 117, (2013) 296-312,
                    147: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
                    148:
                    149: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
                    150: Properties and applications of Fisher distribution on the rotation group,
                    151: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
                    152: Journal of Multivariate Analysis, 116 (2013), 440--455,
                    153: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
                    154:
                    155: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
                    156: Funkcialaj Ekvacioj 56 (2013), 51--61.
1.11      takayama  157: <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
                    158: <!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
1.1       takayama  159:
                    160: <li>
                    161: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
                    162: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
                    163: Holonomic Gradient Descent  and its Application to Fisher-Bingham Integral,
                    164: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a>  -->
                    165: Advances in Applied Mathematics 47 (2011), 639--658,
                    166: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
1.13      takayama  167:
1.1       takayama  168: </ol>
                    169:
1.13      takayama  170: Early papers related to HGM. <br>
                    171: <ol>
                    172: <li>
                    173: H.Dwinwoodie, L.Matusevich, E. Mosteig,
                    174: Transform methods for the hypergeometric distribution,
                    175: Statistics and Computing 14 (2004), 287--297.
                    176: </ol>
                    177:
                    178:
                    179:
1.2       takayama  180: <h2> Three Steps of HGM </h2>
                    181: <ol>
1.10      takayama  182: <li> Finding a holonomic system satisfied by the normalizing constant.
1.2       takayama  183: We may use computational or theoretical methods to find it.
                    184: Groebner basis and related methods are used.
1.10      takayama  185: <li> Finding an initial value vector for the holonomic system.
1.2       takayama  186: This is equivalent to evaluating the normalizing constant and its derivatives
                    187: at a point.
                    188: This step is usually performed by a series expansion.
1.10      takayama  189: <li> Solving the holonomic system numerically. We use several methods
1.2       takayama  190: in numerical analysis such as the Runge-Kutta method of solving
                    191: ordinary differential equations and efficient solvers of systems of linear
                    192: equations.
                    193: </ol>
                    194:
1.1       takayama  195: <h2> Software Packages for HGM</h2>
1.14      takayama  196:
1.15      takayama  197: <ul>
                    198: <li>
1.16      takayama  199: CRAN package <a href="https://cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).
1.14      takayama  200:
1.15      takayama  201: <li>
1.14      takayama  202: Some software packages are experimental and temporary documents are found in
1.6       takayama  203: "asir-contrib manual" (auto-autogenerated part), or
                    204: "Experimental Functions in Asir", or "miscellaneous and other documents"
                    205: of the
                    206: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7       takayama  207: OpenXM documents</a>
1.8       takayama  208: or in <a href="./"> this folder</a>.
1.10      takayama  209: The nightly snapshot of the asir-contrib can be found in the asir page below,
1.6       takayama  210: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8       takayama  211: cvsweb page</a>.
1.1       takayama  212: <ol>
1.9       takayama  213: <li> Command line interfaces are in the folder OpenXM/src/hgm
                    214: in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
                    215: OpenXM distribution page </a>.
1.14      takayama  216: <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  217: To install this package in R, type in
                    218: <pre>
                    219: R CMD install hgm_*.tar.gz
                    220: </pre>
1.10      takayama  221: <li> The following packages are
                    222: for the computer algebra system
                    223: <a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
                    224: They are in the asir-contrib collection.
                    225: <ul>
                    226: <li> yang.rr (for Pfaffian systems) ,
                    227: nk_restriction.rr (for D-module integrations),
                    228: tk_jack.rr  (for Jack polynomials),
                    229: ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
                    230: are for the steps 1 or 2.
                    231: <li> nk_fb_gen_c.rr is a package to generate a C program to perform
1.7       takayama  232: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.10      takayama  233: <li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
                    234: </ul>
1.1       takayama  235: </ol>
                    236:
1.15      takayama  237: </ul>
                    238:
1.1       takayama  239: <h2> Programs to try examples of our papers </h2>
                    240: <ol>
                    241: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
                    242: </ol>
                    243:
1.22    ! takayama  244: <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.21 2016/11/03 23:05:22 takayama Exp $ </pre>
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