=================================================================== RCS file: /home/cvs/OpenXM/src/hgm/doc/ref-hgm.html,v retrieving revision 1.5 retrieving revision 1.11 diff -u -p -r1.5 -r1.11 --- OpenXM/src/hgm/doc/ref-hgm.html 2014/03/26 05:02:18 1.5 +++ OpenXM/src/hgm/doc/ref-hgm.html 2014/05/20 02:12:18 1.11 @@ -12,6 +12,18 @@ the Holonomic Gradient Descent Method (HGD)

Papers and Tutorials

    +
  1. N.Marumo, T.Oaku, A.Takemura, +Properties of powers of functions satisfying second-order linear differential equations with applications to statistics, + arxiv:1405.4451 + +
  2. J.Hayakawa, A.Takemura, +Estimation of exponential-polynomial distribution by holonomic gradient descent + arxiv:1403.7852 + +
  3. C.Siriteanu, A.Takemura, S.Kuriki, +MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method + arxiv:1403.3788 +
  4. T.Koyama, Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra, arxiv:1311.6905 @@ -43,7 +55,8 @@ Calculation of Orthant Probabilities by the Holonomic
  5. T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama, Holonomic Rank of the Fisher-Bingham System of Differential Equations, -to appear in Journal of Pure and Applied Algebra +Journal of Pure and Applied Algebra (online), + DOI
  6. T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama, @@ -66,8 +79,8 @@ Journal of Multivariate Analysis, 116 (2013), 440--455
  7. T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral, Funkcialaj Ekvacioj 56 (2013), 51--61. - -jstage +DOI +
  8. Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara, @@ -80,30 +93,53 @@ Advances in Applied Mathematics 47 (2011), 639--658,

    Three Steps of HGM

      -
    1. Find a holonomic system satisfied by the normalizing constant. +
    2. 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. -
    3. Find an initial value vector for the holonomic system. +
    4. 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. -
    5. Solve the holonomic system numerically. We use several methods +
    6. 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.

    Software Packages for HGM

    +Most 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 + +OpenXM documents +or in this folder. +The nightly snapshot of the asir-contrib can be found in the asir page below, +or look up our +cvsweb page.
      -
    1. hgm package for R for the step 3. -
    2. 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 - asir-contrib -
    3. nk_fb_gen_c 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 - asir-contrib +
    4. Command line interfaces are in the folder OpenXM/src/hgm +in the OpenXM source tree. See +OpenXM distribution page . +
    5. hgm package for R (hgm_*tar.gz, hgm-manual.pdf) for the step 3. +To install this package in R, type in +
      +R CMD install hgm_*.tar.gz
+
      +
    6. The following packages are +for the computer algebra system + Risa/Asir. +They are in the asir-contrib collection. +
        +
      • 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. +
      • 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). +
      • ot_hgm_ahg.rr (HGM for A-distributions, very experimental). +

    Programs to try examples of our papers

    @@ -111,6 +147,6 @@ It is in the
  9. d-dimensional Fisher-Bingham System
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