=================================================================== RCS file: /home/cvs/OpenXM/src/hgm/doc/ref-hgm.html,v retrieving revision 1.1 retrieving revision 1.15 diff -u -p -r1.1 -r1.15 --- OpenXM/src/hgm/doc/ref-hgm.html 2014/03/24 06:43:55 1.1 +++ OpenXM/src/hgm/doc/ref-hgm.html 2016/02/07 06:53:00 1.15 @@ -3,7 +3,7 @@ References for HGM - + @@ -12,7 +12,68 @@ the Holonomic Gradient Descent Method (HGD)

Papers and Tutorials

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  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. +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 + + +
  10. N.Marumo, T.Oaku, A.Takemura, +Properties of powers of functions satisfying second-order linear differential equations with applications to statistics, + arxiv:1405.4451 + +
  11. J.Hayakawa, A.Takemura, +Estimation of exponential-polynomial distribution by holonomic gradient descent + arxiv:1403.7852 + +
  12. C.Siriteanu, A.Takemura, S.Kuriki, +MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method + arxiv:1403.3788 + +
  13. T.Koyama, Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra, arxiv:1311.6905 @@ -30,15 +91,21 @@ T.Hibi et al, Groebner Bases : Statistics and Software Introduction to the Holonomic Gradient Method (movie), 2013. movie at youtube +
  14. T.Sei, A.Kume, -Calculating the normalising constant of the Bingham distribution on the sphere using the holonomic gradient method, +Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method, Statistics and Computing, 2013, DOI +
  15. T.Koyama, A.Takemura, +Calculation of Orthant Probabilities by the Holonomic Gradient Method, + arxiv:1211.6822 +
  16. 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
  17. T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama, @@ -61,8 +128,8 @@ Journal of Multivariate Analysis, 116 (2013), 440--455
  18. T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral, Funkcialaj Ekvacioj 56 (2013), 51--61. - -jstage +DOI +
  19. Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara, @@ -71,21 +138,83 @@ Holonomic Gradient Descent and its Application to Fis Advances in Applied Mathematics 47 (2011), 639--658, DOI +
+Early papers related to HGM.
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  1. +H.Dwinwoodie, L.Matusevich, E. Mosteig, +Transform methods for the hypergeometric distribution, +Statistics and Computing 14 (2004), 287--297. +
+ + + +

Three Steps of HGM

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  1. 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. +
  2. 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. +
  3. 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. +
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Software Packages for HGM

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Programs to try examples of our papers

  1. d-dimensional Fisher-Bingham System
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