=================================================================== RCS file: /home/cvs/OpenXM/src/hgm/doc/ref-hgm.html,v retrieving revision 1.12 retrieving revision 1.25 diff -u -p -r1.12 -r1.25 --- OpenXM/src/hgm/doc/ref-hgm.html 2016/02/05 01:58:34 1.12 +++ OpenXM/src/hgm/doc/ref-hgm.html 2018/05/07 04:50:46 1.25 @@ -3,7 +3,7 @@ References for HGM - + @@ -12,10 +12,89 @@ the Holonomic Gradient Descent Method (HGD)

Papers and Tutorials

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  1. Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama, Nobuki Takayama, +Holonomic Gradient Method for Two Way Contingency Tables, + arxiv:1803.04170 +
  2. F.H.Danufane, K.Ohara, N.Takayama, C.Siriteanu, +Holonomic Gradient Method-Based CDF Evaluation for the Largest Eigenvalue of a Complex Noncentral Wishart Matrix +(Title of the version 1: Holonomic Gradient Method for the Distribution Function of the Largest Root of Complex Non-central Wishart Matrices), + arxiv:1707.02564 +
  3. T.Koyama, +An integral formula for the powered sum of the independent, identically and normally distributed random variables, + arxiv:1706.03989 +
  4. H.Hashiguchi, N.Takayama, A.Takemura, +Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability +by Holonomic Gradient Method, + arxiv:1610.09187 + +
  5. R.Vidunas, A.Takemura, +Differential relations for the largest root distribution +of complex non-central Wishart matrices, + arxiv:1609.01799 + +
  6. S.Mano, +The A-hypergeometric System Associated with the Rational Normal Curve and +Exchangeable Structures, + arxiv:1607.03569 + +
  7. M.Noro, +System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions, + ACM DL +
  8. 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 + arxiv:1602.01637 +
  9. T.Koyama, +Holonomic gradient method for the probability content of a simplex +region +with a multivariate normal distribution, + arxiv:1512.06564 + + +
  10. N.Takayama, S.Kuriki, A.Takemura, +A-Hpergeometric Distributions and Newton Polytopes, + arxiv:1510.02269 + +
  11. G.Weyenberg, R.Yoshida, D.Howe, +Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace, + arxiv:1506.00142 + +
  12. 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, + arxiv:1507.07056 + +
  13. K.Ohara, N.Takayama, +Pfaffian Systems of A-Hypergeometric Systems II --- +Holonomic Gradient Method, + arxiv:1505.02947 + +
  14. T.Koyama, +The Annihilating Ideal of the Fisher Integral, + arxiv:1503.05261 + +
  15. T.Koyama, A.Takemura, +Holonomic gradient method for distribution function of a weighted sum +of noncentral chi-square random variables, + arxiv:1503.00378 + +
  16. Y.Goto, +Contiguity relations of Lauricella's F_D revisited, + arxiv:1412.3256 + +
  17. +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. + +DOI + +
  18. N.Marumo, T.Oaku, A.Takemura, Properties of powers of functions satisfying second-order linear differential equations with applications to statistics, arxiv:1405.4451 @@ -36,7 +115,9 @@ Holonomic Modules Associated with Multivariate Normal Pfaffian Systems of A-Hypergeometric Equations I, Bases of Twisted Cohomology Groups, arxiv:1212.6103 -(major revision v2 of arxiv:1212.6103) +(major revision v2 of arxiv:1212.6103). +Accepted version is at + DOI
  19. Intro @@ -93,8 +174,19 @@ 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. Finding a holonomic system satisfied by the normalizing constant. @@ -111,7 +203,13 @@ equations.

Software Packages for HGM

-Most software packages are experimental and temporary documents are found in + + + +

Programs to try examples of our papers

  1. d-dimensional Fisher-Bingham System
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