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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>
1.27    ! takayama   15: <li> M.Harkonen, T.Sei, Y.Hirose,
        !            16: Holonomic extended least angle regression,
        !            17: <a href="https://arxiv.org/abs/1809.08190"> arxiv:1809.08190 </a>
        !            18: <li> S.Mano,
        !            19: Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics,
        !            20: <a href="https://www.springer.com/jp/book/9784431558866">
        !            21: JSS Research Series in Statistics</a>, 2018.
1.26      takayama   22: <li> A.Kume, T.Sei,
                     23: On the exact maximum likelihood inference of Fisher–Bingham distributions using an adjusted holonomic gradient method,
                     24: <a href="https://doi.org/10.1007/s11222-017-9765-3"> doi </a> (2018)
1.24      takayama   25: <li> Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama, Nobuki Takayama,
                     26: Holonomic Gradient Method for Two Way Contingency Tables,
1.25      takayama   27: <a href="https://arxiv.org/abs/1803.04170"> arxiv:1803.04170 </a>
                     28: <li> F.H.Danufane, K.Ohara, N.Takayama, C.Siriteanu,
                     29: Holonomic Gradient Method-Based CDF Evaluation for the Largest Eigenvalue of a Complex Noncentral Wishart Matrix
                     30: (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   31: <a href="https://arxiv.org/abs/1707.02564"> arxiv:1707.02564 </a>
                     32: <li> T.Koyama,
                     33: An integral formula for the powered sum of the independent, identically and normally distributed random variables,
                     34: <a href="https://arxiv.org/abs/1706.03989"> arxiv:1706.03989 </a>
1.21      takayama   35: <li> H.Hashiguchi, N.Takayama, A.Takemura,
                     36: Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability
                     37: by Holonomic Gradient Method,
                     38: <a href="https://arxiv.org/abs/1610.09187"> arxiv:1610.09187 </a>
                     39:
1.18      takayama   40: <li> R.Vidunas, A.Takemura,
                     41: Differential relations for the largest root distribution
                     42: of complex non-central Wishart matrices,
                     43: <a href="http://arxiv.org/abs/1609.01799"> arxiv:1609.01799 </a>
                     44:
1.20      takayama   45: <li> S.Mano,
                     46: The A-hypergeometric System Associated with the Rational Normal Curve and
                     47: Exchangeable Structures,
                     48: <a href="http://arxiv.org/abs/1607.03569"> arxiv:1607.03569 </a>
                     49:
1.19      takayama   50: <li> M.Noro,
                     51: System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions,
                     52: <a href="http://dl.acm.org/citation.cfm?doid=2930889.2930905"> ACM DL </a>
                     53:
1.12      takayama   54: <li> Y.Goto, K.Matsumoto,
                     55: Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications,
1.13      takayama   56: <a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637 </a>
                     57:
                     58: <li>  T.Koyama,
                     59: Holonomic gradient method for the probability content of a simplex
                     60: region
                     61: with a multivariate normal distribution,
                     62: <a href="http://arxiv.org/abs/1512.06564">  arxiv:1512.06564 </a>
                     63:
                     64:
                     65: <li> N.Takayama, S.Kuriki, A.Takemura,
                     66: A-Hpergeometric Distributions and Newton Polytopes,
                     67: <a href="http://arxiv.org/abs/1510.02269">  arxiv:1510.02269 </a>
                     68:
                     69: <li> G.Weyenberg, R.Yoshida, D.Howe,
                     70: Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace,
                     71: <a href="http://arxiv.org/abs/1506.00142"> arxiv:1506.00142 </a>
                     72:
1.17      takayama   73: <li> C.Siriteanu, A.Takemura, C.Koutschan, S.Kuriki, D.St.P.Richards, H.Sin,
                     74: Exact ZF Analysis and Computer-Algebra-Aided Evaluation
                     75: in Rank-1 LoS Rician Fading,
                     76: <a href="http://arxiv.org/abs/1507.07056"> arxiv:1507.07056 </a>
                     77:
1.13      takayama   78: <li> K.Ohara, N.Takayama,
                     79: Pfaffian Systems of A-Hypergeometric Systems II ---
                     80: Holonomic Gradient Method,
                     81: <a href="http://arxiv.org/abs/1505.02947"> arxiv:1505.02947 </a>
                     82:
                     83: <li> T.Koyama,
                     84: The Annihilating Ideal of the Fisher Integral,
                     85: <a href="http://arxiv.org/abs/1503.05261"> arxiv:1503.05261 </a>
                     86:
                     87: <li> T.Koyama, A.Takemura,
                     88: Holonomic gradient method for distribution function of a weighted sum
                     89: of noncentral chi-square random variables,
                     90: <a href="http://arxiv.org/abs/1503.00378"> arxiv:1503.00378 </a>
                     91:
                     92: <li> Y.Goto,
                     93: Contiguity relations of Lauricella's F_D revisited,
                     94: <a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a>
1.12      takayama   95:
1.15      takayama   96: <li>
                     97: T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama,
                     98: Software Packages for Holonomic Gradient Method,
                     99: Mathematial Software --- ICMS 2014,
                    100: 4th International Conference, Proceedings.
                    101: Edited by Hoon Hong and Chee Yap,
                    102: Springer lecture notes in computer science 8592,
                    103: 706--712.
                    104: <a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_105">
                    105: DOI
                    106: </a>
                    107:
1.11      takayama  108: <li>N.Marumo, T.Oaku, A.Takemura,
                    109: Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
                    110: <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
                    111:
1.8       takayama  112: <li> J.Hayakawa, A.Takemura,
                    113: Estimation of exponential-polynomial distribution by holonomic gradient descent
                    114: <a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>
                    115:
                    116: <li> C.Siriteanu, A.Takemura, S.Kuriki,
                    117: MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method
                    118: <a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>
                    119:
1.4       takayama  120: <li> T.Koyama,
1.1       takayama  121: Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
                    122: <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>
                    123:
                    124: <li> T.Hibi, K.Nishiyama, N.Takayama,
                    125: Pfaffian Systems of A-Hypergeometric Equations I,
                    126: Bases of Twisted Cohomology Groups,
                    127: <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
1.22      takayama  128: (major revision v2 of arxiv:1212.6103).
                    129: Accepted version is at
                    130: <a href="http://dx.doi.org/10.1016/j.aim.2016.10.021"> DOI </a>
1.1       takayama  131:
                    132: <li> <img src="./wakaba01.png" alt="Intro">
                    133: <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
                    134: T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.
                    135:
                    136: <li> <img src="./wakaba01.png" alt="Intro">
                    137: Introduction to the Holonomic Gradient Method (movie), 2013.
                    138: <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
                    139:
1.2       takayama  140:
1.1       takayama  141: <li> T.Sei, A.Kume,
1.2       takayama  142: Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
1.1       takayama  143: Statistics and Computing, 2013,
                    144: <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
                    145:
1.4       takayama  146: <li> T.Koyama, A.Takemura,
1.2       takayama  147: Calculation of Orthant Probabilities by the Holonomic Gradient Method,
                    148: <a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>
                    149:
1.1       takayama  150: <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
                    151: Holonomic Rank of the Fisher-Bingham System of Differential Equations,
                    152: <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
1.11      takayama  153: Journal of Pure and Applied Algebra  (online),
                    154: <a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a>
1.1       takayama  155:
                    156: <li>
                    157: T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
                    158: Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
                    159: <!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
                    160: Computational Statistics (2013)
                    161: <a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>
                    162:
                    163: <li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
                    164: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
                    165: <!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
                    166: Journal of Multivariate Analysis, 117, (2013) 296-312,
                    167: <a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a>
                    168:
                    169: <li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
                    170: Properties and applications of Fisher distribution on the rotation group,
                    171: <!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
                    172: Journal of Multivariate Analysis, 116 (2013), 440--455,
                    173: <a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>
                    174:
                    175: <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
                    176: Funkcialaj Ekvacioj 56 (2013), 51--61.
1.11      takayama  177: <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a>
                    178: <!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> -->
1.1       takayama  179:
                    180: <li>
                    181: Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
                    182: Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
                    183: Holonomic Gradient Descent  and its Application to Fisher-Bingham Integral,
                    184: <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a>  -->
                    185: Advances in Applied Mathematics 47 (2011), 639--658,
                    186: <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
1.13      takayama  187:
1.1       takayama  188: </ol>
                    189:
1.13      takayama  190: Early papers related to HGM. <br>
                    191: <ol>
                    192: <li>
                    193: H.Dwinwoodie, L.Matusevich, E. Mosteig,
                    194: Transform methods for the hypergeometric distribution,
                    195: Statistics and Computing 14 (2004), 287--297.
                    196: </ol>
                    197:
                    198:
                    199:
1.2       takayama  200: <h2> Three Steps of HGM </h2>
                    201: <ol>
1.10      takayama  202: <li> Finding a holonomic system satisfied by the normalizing constant.
1.2       takayama  203: We may use computational or theoretical methods to find it.
                    204: Groebner basis and related methods are used.
1.10      takayama  205: <li> Finding an initial value vector for the holonomic system.
1.2       takayama  206: This is equivalent to evaluating the normalizing constant and its derivatives
                    207: at a point.
                    208: This step is usually performed by a series expansion.
1.10      takayama  209: <li> Solving the holonomic system numerically. We use several methods
1.2       takayama  210: in numerical analysis such as the Runge-Kutta method of solving
                    211: ordinary differential equations and efficient solvers of systems of linear
                    212: equations.
                    213: </ol>
                    214:
1.1       takayama  215: <h2> Software Packages for HGM</h2>
1.14      takayama  216:
1.15      takayama  217: <ul>
                    218: <li>
1.16      takayama  219: CRAN package <a href="https://cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).
1.14      takayama  220:
1.15      takayama  221: <li>
1.14      takayama  222: Some software packages are experimental and temporary documents are found in
1.6       takayama  223: "asir-contrib manual" (auto-autogenerated part), or
                    224: "Experimental Functions in Asir", or "miscellaneous and other documents"
                    225: of the
                    226: <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
1.7       takayama  227: OpenXM documents</a>
1.8       takayama  228: or in <a href="./"> this folder</a>.
1.10      takayama  229: The nightly snapshot of the asir-contrib can be found in the asir page below,
1.6       takayama  230: or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">
1.8       takayama  231: cvsweb page</a>.
1.1       takayama  232: <ol>
1.9       takayama  233: <li> Command line interfaces are in the folder OpenXM/src/hgm
                    234: in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
                    235: OpenXM distribution page </a>.
1.14      takayama  236: <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  237: To install this package in R, type in
                    238: <pre>
                    239: R CMD install hgm_*.tar.gz
                    240: </pre>
1.10      takayama  241: <li> The following packages are
                    242: for the computer algebra system
                    243: <a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
                    244: They are in the asir-contrib collection.
                    245: <ul>
                    246: <li> yang.rr (for Pfaffian systems) ,
                    247: nk_restriction.rr (for D-module integrations),
                    248: tk_jack.rr  (for Jack polynomials),
                    249: ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),
                    250: are for the steps 1 or 2.
                    251: <li> nk_fb_gen_c.rr is a package to generate a C program to perform
1.7       takayama  252: maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).
1.10      takayama  253: <li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
                    254: </ul>
1.1       takayama  255: </ol>
                    256:
1.15      takayama  257: </ul>
                    258:
1.1       takayama  259: <h2> Programs to try examples of our papers </h2>
                    260: <ol>
                    261: <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
                    262: </ol>
                    263:
1.27    ! takayama  264: <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.26 2018/07/06 06:01:51 takayama Exp $ </pre>
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