=================================================================== RCS file: /home/cvs/OpenXM/src/hgm/doc/ref-hgm.html,v retrieving revision 1.8 retrieving revision 1.13 diff -u -p -r1.8 -r1.13 --- OpenXM/src/hgm/doc/ref-hgm.html 2014/04/03 07:34:31 1.8 +++ OpenXM/src/hgm/doc/ref-hgm.html 2016/02/05 21:42:46 1.13 @@ -3,7 +3,7 @@ References for HGM - + @@ -12,6 +12,47 @@ the Holonomic Gradient Descent Method (HGD)

Papers and Tutorials

    +
  1. Y.Goto, K.Matsumoto, +Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications, + arxiv:1602.01637 + +
  2. T.Koyama, +Holonomic gradient method for the probability content of a simplex +region +with a multivariate normal distribution, + arxiv:1512.06564 + + +
  3. N.Takayama, S.Kuriki, A.Takemura, +A-Hpergeometric Distributions and Newton Polytopes, + arxiv:1510.02269 + +
  4. G.Weyenberg, R.Yoshida, D.Howe, +Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace, + arxiv:1506.00142 + +
  5. K.Ohara, N.Takayama, +Pfaffian Systems of A-Hypergeometric Systems II --- +Holonomic Gradient Method, + arxiv:1505.02947 + +
  6. T.Koyama, +The Annihilating Ideal of the Fisher Integral, + arxiv:1503.05261 + +
  7. T.Koyama, A.Takemura, +Holonomic gradient method for distribution function of a weighted sum +of noncentral chi-square random variables, + arxiv:1503.00378 + +
  8. Y.Goto, +Contiguity relations of Lauricella's F_D revisited, + arxiv:1412.3256 + +
  9. N.Marumo, T.Oaku, A.Takemura, +Properties of powers of functions satisfying second-order linear differential equations with applications to statistics, + arxiv:1405.4451 +
  10. J.Hayakawa, A.Takemura, Estimation of exponential-polynomial distribution by holonomic gradient descent arxiv:1403.7852 @@ -51,7 +92,8 @@ Calculation of Orthant Probabilities by the Holonomic
  11. 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
  12. T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama, @@ -74,8 +116,8 @@ Journal of Multivariate Analysis, 116 (2013), 440--455
  13. T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral, Funkcialaj Ekvacioj 56 (2013), 51--61. - -jstage +DOI +
  14. Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara, @@ -84,18 +126,29 @@ Holonomic Gradient Descent and its Application to Fis Advances in Applied Mathematics 47 (2011), 639--658, DOI +
+Early papers related to HGM.
+
    +
  1. +H.Dwinwoodie, L.Matusevich, E. Mosteig, +Transform methods for the hypergeometric distribution, +Statistics and Computing 14 (2004), 287--297. +
+ + +

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. @@ -109,19 +162,32 @@ of the OpenXM documents or in this folder. -The nightly snapshot of the asir-contrib can be found in the Asir-Contrib page below, +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 +
    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). -It is in the - asir-contrib. +
      • ot_hgm_ahg.rr (HGM for A-distributions, very experimental). +

    Programs to try examples of our papers

    @@ -129,6 +195,6 @@ It is in the
  7. d-dimensional Fisher-Bingham System
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