=================================================================== RCS file: /home/cvs/OpenXM/src/hgm/doc/ref-hgm.html,v retrieving revision 1.7 retrieving revision 1.22 diff -u -p -r1.7 -r1.22 --- OpenXM/src/hgm/doc/ref-hgm.html 2014/03/31 07:23:09 1.7 +++ OpenXM/src/hgm/doc/ref-hgm.html 2016/11/03 23:19:18 1.22 @@ -3,7 +3,7 @@ <head> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> <title>References for HGM</title> <!-- Use UTF-8 譁�ｭ� code--> -<!-- Do not edit this file. Edit it under misc-2012/09/keisan-1/ref.html. --> +<!-- Do not edit this file. Edit it under OpenXM/src/hgm/doc --> </head> <body> @@ -12,6 +12,91 @@ the Holonomic Gradient Descent Method (HGD) </h1> <h2> Papers and Tutorials</h2> <ol> +<li> H.Hashiguchi, N.Takayama, A.Takemura, +Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability +by Holonomic Gradient Method, +<a href="https://arxiv.org/abs/1610.09187"> arxiv:1610.09187 </a> + +<li> R.Vidunas, A.Takemura, +Differential relations for the largest root distribution +of complex non-central Wishart matrices, +<a href="http://arxiv.org/abs/1609.01799"> arxiv:1609.01799 </a> + +<li> S.Mano, +The A-hypergeometric System Associated with the Rational Normal Curve and +Exchangeable Structures, +<a href="http://arxiv.org/abs/1607.03569"> arxiv:1607.03569 </a> + +<li> M.Noro, +System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions, +<a href="http://dl.acm.org/citation.cfm?doid=2930889.2930905"> ACM DL </a> + +<li> Y.Goto, K.Matsumoto, +Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications, +<a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637 </a> + +<li> T.Koyama, +Holonomic gradient method for the probability content of a simplex +region +with a multivariate normal distribution, +<a href="http://arxiv.org/abs/1512.06564"> arxiv:1512.06564 </a> + + +<li> N.Takayama, S.Kuriki, A.Takemura, +A-Hpergeometric Distributions and Newton Polytopes, +<a href="http://arxiv.org/abs/1510.02269"> arxiv:1510.02269 </a> + +<li> G.Weyenberg, R.Yoshida, D.Howe, +Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace, +<a href="http://arxiv.org/abs/1506.00142"> arxiv:1506.00142 </a> + +<li> C.Siriteanu, A.Takemura, C.Koutschan, S.Kuriki, D.St.P.Richards, H.Sin, +Exact ZF Analysis and Computer-Algebra-Aided Evaluation +in Rank-1 LoS Rician Fading, +<a href="http://arxiv.org/abs/1507.07056"> arxiv:1507.07056 </a> + +<li> K.Ohara, N.Takayama, +Pfaffian Systems of A-Hypergeometric Systems II --- +Holonomic Gradient Method, +<a href="http://arxiv.org/abs/1505.02947"> arxiv:1505.02947 </a> + +<li> T.Koyama, +The Annihilating Ideal of the Fisher Integral, +<a href="http://arxiv.org/abs/1503.05261"> arxiv:1503.05261 </a> + +<li> T.Koyama, A.Takemura, +Holonomic gradient method for distribution function of a weighted sum +of noncentral chi-square random variables, +<a href="http://arxiv.org/abs/1503.00378"> arxiv:1503.00378 </a> + +<li> Y.Goto, +Contiguity relations of Lauricella's F_D revisited, +<a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a> + +<li> +T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama, +Software Packages for Holonomic Gradient Method, +Mathematial Software --- ICMS 2014, +4th International Conference, Proceedings. +Edited by Hoon Hong and Chee Yap, +Springer lecture notes in computer science 8592, +706--712. +<a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_105"> +DOI +</a> + +<li>N.Marumo, T.Oaku, A.Takemura, +Properties of powers of functions satisfying second-order linear differential equations with applications to statistics, +<a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a> + +<li> J.Hayakawa, A.Takemura, +Estimation of exponential-polynomial distribution by holonomic gradient descent +<a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a> + +<li> C.Siriteanu, A.Takemura, S.Kuriki, +MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method +<a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a> + <li> T.Koyama, Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra, <a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a> @@ -20,7 +105,9 @@ Holonomic Modules Associated with Multivariate Normal Pfaffian Systems of A-Hypergeometric Equations I, Bases of Twisted Cohomology Groups, <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a> -(major revision v2 of arxiv:1212.6103) +(major revision v2 of arxiv:1212.6103). +Accepted version is at +<a href="http://dx.doi.org/10.1016/j.aim.2016.10.021"> DOI </a> <li> <img src="./wakaba01.png" alt="Intro"> <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3"> @@ -43,7 +130,8 @@ Calculation of Orthant Probabilities by the Holonomic <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama, Holonomic Rank of the Fisher-Bingham System of Differential Equations, <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>--> -to appear in Journal of Pure and Applied Algebra +Journal of Pure and Applied Algebra (online), +<a href="http://dx.doi.org/10.1016/j.jpaa.2014.03.004"> DOI </a> <li> T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama, @@ -66,8 +154,8 @@ Journal of Multivariate Analysis, 116 (2013), 440--455 <li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral, Funkcialaj Ekvacioj 56 (2013), 51--61. -<!-- <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a> --> -<a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> +<a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a> +<!-- <a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a> --> <li> Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara, @@ -76,51 +164,83 @@ Holonomic Gradient Descent and its Application to Fis <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a> --> Advances in Applied Mathematics 47 (2011), 639--658, <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a> + </ol> +Early papers related to HGM. <br> +<ol> +<li> +H.Dwinwoodie, L.Matusevich, E. Mosteig, +Transform methods for the hypergeometric distribution, +Statistics and Computing 14 (2004), 287--297. +</ol> + + + <h2> Three Steps of HGM </h2> <ol> -<li> Find a holonomic system satisfied by the normalizing constant. +<li> Finding a holonomic system satisfied by the normalizing constant. We may use computational or theoretical methods to find it. Groebner basis and related methods are used. -<li> Find an initial value vector for the holonomic system. +<li> Finding an initial value vector for the holonomic system. This is equivalent to evaluating the normalizing constant and its derivatives at a point. This step is usually performed by a series expansion. -<li> Solve the holonomic system numerically. We use several methods +<li> Solving the holonomic system numerically. We use several methods in numerical analysis such as the Runge-Kutta method of solving ordinary differential equations and efficient solvers of systems of linear equations. </ol> <h2> Software Packages for HGM</h2> -Most software packages are experimental and temporary documents are found in + +<ul> +<li> +CRAN package <a href="https://cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R). + +<li> +Some software packages are experimental and temporary documents are found in "asir-contrib manual" (auto-autogenerated part), or "Experimental Functions in Asir", or "miscellaneous and other documents" of the <a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html"> OpenXM documents</a> -or in <a href="./"> this folder </a>. -The nightly snapshot of the asir-contrib can be found in the Asir-Contrib page below, +or in <a href="./"> this folder</a>. +The nightly snapshot of the asir-contrib can be found in the asir page below, or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/"> -cvsweb page </a> +cvsweb page</a>. <ol> -<li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/hgm/"> hgm package for R </a> for the step 3. -<li> yang (for Pfaffian systems) , nk_restriction (for D-module integrations), -tk_jack (for Jack polynomials), ko_fb_pfaffian (Pfaffian system for the Fisher-Bingham system) -are for the steps 1 or 2 and in the -<a href="http://www.math.kobe-u.ac.jp/Asir"> asir-contrib </a> -<li> nk_fb_gen_c is a package to generate a C program to perform +<li> Command line interfaces are in the folder OpenXM/src/hgm +in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM"> +OpenXM distribution page </a>. +<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. +To install this package in R, type in +<pre> +R CMD install hgm_*.tar.gz +</pre> +<li> The following packages are +for the computer algebra system +<a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>. +They are in the asir-contrib collection. +<ul> +<li> yang.rr (for Pfaffian systems) , +nk_restriction.rr (for D-module integrations), +tk_jack.rr (for Jack polynomials), +ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system), +are for the steps 1 or 2. +<li> nk_fb_gen_c.rr is a package to generate a C program to perform maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent). -It is in the -<a href="http://www.math.kobe-u.ac.jp/Asir"> asir-contrib </a> +<li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental). +</ul> </ol> +</ul> + <h2> Programs to try examples of our papers </h2> <ol> <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a> </ol> -<pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.6 2014/03/28 03:02:36 takayama Exp $ </pre> +<pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.21 2016/11/03 23:05:22 takayama Exp $ </pre> </body> </html>