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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>
1.12      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:
1.15    ! takayama   52: <li>
        !            53: T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama,
        !            54: Software Packages for Holonomic Gradient Method,
        !            55: Mathematial Software --- ICMS 2014,
        !            56: 4th International Conference, Proceedings.
        !            57: Edited by Hoon Hong and Chee Yap,
        !            58: Springer lecture notes in computer science 8592,
        !            59: 706--712.
        !            60: <a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_105">
        !            61: DOI
        !            62: </a>
        !            63:
1.11      takayama   64: <li>N.Marumo, T.Oaku, A.Takemura,
                     65: Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
                     66: <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
                     67:
1.8       takayama   68: <li> J.Hayakawa, A.Takemura,
                     69: Estimation of exponential-polynomial distribution by holonomic gradient descent
                     70: <a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
                     71:
                     72: <li> C.Siriteanu, A.Takemura, S.Kuriki,
                     73: MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
                     74: <a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
                     75:
1.4       takayama   76: <li> T.Koyama,
1.1       takayama   77: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
                     78: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
                     79:
                     80: <li> T.Hibi, K.Nishiyama, N.Takayama,
                     81: Pfaffian Systems of A-Hypergeometric Equations I,
                     82: Bases of Twisted Cohomology Groups,
                     83: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
                     84: (major revision v2 of arxiv:1212.6103)
                     85:
                     86: <li> <img src="./wakaba01.png" alt="Intro">
                     87: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
                     88: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
                     89:
                     90: <li> <img src="./wakaba01.png" alt="Intro">
                     91: Introduction to the Holonomic Gradient Method (movie), 2013.
                     92: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
                     93:
1.2       takayama   94:
1.1       takayama   95: <li> T.Sei, A.Kume,
1.2       takayama   96: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1       takayama   97: Statistics and Computing, 2013,
                     98: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
                     99:
1.4       takayama  100: <li> T.Koyama, A.Takemura,
1.2       takayama  101: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
                    102: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
                    103:
1.1       takayama  104: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
                    105: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
                    106: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
1.11      takayama  107: Journal of Pure and Applied Algebra  (online),
                    108: <a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
1.1       takayama  109:
                    110: <li>
                    111: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
                    112: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
                    113: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
                    114: Computational Statistics (2013)
                    115: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
                    116:
                    117: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
                    118: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
                    119: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
                    120: Journal of Multivariate Analysis, 117, (2013) 296-312,
                    121: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
                    122:
                    123: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
                    124: Properties and applications of Fisher distribution on the rotation group,
                    125: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
                    126: Journal of Multivariate Analysis, 116 (2013), 440--455,
                    127: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
                    128:
                    129: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
                    130: Funkcialaj Ekvacioj 56 (2013), 51--61.
1.11      takayama  131: <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
                    132: <!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
1.1       takayama  133:
                    134: <li>
                    135: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
                    136: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
                    137: Holonomic Gradient Descent  and its Application to Fisher-Bingham Integral,
                    138: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a>  -->
                    139: Advances in Applied Mathematics 47 (2011), 639--658,
                    140: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
1.13      takayama  141:
1.1       takayama  142: </ol>
                    143:
1.13      takayama  144: Early papers related to HGM. <br>
                    145: <ol>
                    146: <li>
                    147: H.Dwinwoodie, L.Matusevich, E. Mosteig,
                    148: Transform methods for the hypergeometric distribution,
                    149: Statistics and Computing 14 (2004), 287--297.
                    150: </ol>
                    151:
                    152:
                    153:
1.2       takayama  154: <h2> Three Steps of HGM </h2>
                    155: <ol>
1.10      takayama  156: <li> Finding a holonomic system satisfied by the normalizing constant.
1.2       takayama  157: We may use computational or theoretical methods to find it.
                    158: Groebner basis and related methods are used.
1.10      takayama  159: <li> Finding an initial value vector for the holonomic system.
1.2       takayama  160: This is equivalent to evaluating the normalizing constant and its derivatives
                    161: at a point.
                    162: This step is usually performed by a series expansion.
1.10      takayama  163: <li> Solving the holonomic system numerically. We use several methods
1.2       takayama  164: in numerical analysis such as the Runge-Kutta method of solving
                    165: ordinary differential equations and efficient solvers of systems of linear
                    166: equations.
                    167: </ol>
                    168:
1.1       takayama  169: <h2> Software Packages for HGM</h2>
1.14      takayama  170:
1.15    ! takayama  171: <ul>
        !           172: <li>
1.14      takayama  173: CRAN package <a href="https//cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).
                    174:
1.15    ! takayama  175: <li>
1.14      takayama  176: Some software packages are experimental and temporary documents are found in
1.6       takayama  177: "asir-contrib manual" (auto-autogenerated part), or
                    178: "Experimental Functions in Asir", or "miscellaneous and other documents"
                    179: of the
                    180: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7       takayama  181: OpenXM documents</a>
1.8       takayama  182: or in <a href="./"> this folder</a>.
1.10      takayama  183: The nightly snapshot of the asir-contrib can be found in the asir page below,
1.6       takayama  184: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8       takayama  185: cvsweb page</a>.
1.1       takayama  186: <ol>
1.9       takayama  187: <li> Command line interfaces are in the folder OpenXM/src/hgm
                    188: in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
                    189: OpenXM distribution page </a>.
1.14      takayama  190: <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  191: To install this package in R, type in
                    192: <pre>
                    193: R CMD install hgm_*.tar.gz
                    194: </pre>
1.10      takayama  195: <li> The following packages are
                    196: for the computer algebra system
                    197: <a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
                    198: They are in the asir-contrib collection.
                    199: <ul>
                    200: <li> yang.rr (for Pfaffian systems) ,
                    201: nk_restriction.rr (for D-module integrations),
                    202: tk_jack.rr  (for Jack polynomials),
                    203: ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
                    204: are for the steps 1 or 2.
                    205: <li> nk_fb_gen_c.rr is a package to generate a C program to perform
1.7       takayama  206: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.10      takayama  207: <li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
                    208: </ul>
1.1       takayama  209: </ol>
                    210:
1.15    ! takayama  211: </ul>
        !           212:
1.1       takayama  213: <h2> Programs to try examples of our papers </h2>
                    214: <ol>
                    215: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
                    216: </ol>
                    217:
1.15    ! takayama  218: <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.14 2016/02/07 05:18:20 takayama Exp $ </pre>
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