=================================================================== RCS file: /home/cvs/OpenXM/src/hgm/doc/ref-hgm.html,v retrieving revision 1.10 retrieving revision 1.32 diff -u -p -r1.10 -r1.32 --- OpenXM/src/hgm/doc/ref-hgm.html 2014/05/16 11:30:31 1.10 +++ OpenXM/src/hgm/doc/ref-hgm.html 2020/08/24 23:24:27 1.32 @@ -2,8 +2,10 @@ + + References for HGM - + @@ -12,6 +14,118 @@ the Holonomic Gradient Descent Method (HGD)

Papers and Tutorials

    +
  1. M.Adamer, A.Lorincz, A.L.Sattelberger, B.Sturmfels, Algebraic Analysis of Rotation Data + arxiv: 1912.00396 +
  2. +Anna-Laura Sattelberger, Bernd Sturmfels, +D-Modules and Holonomic Functions + arxiv:1910.01395 +
  3. +N.Takayama, L.Jiu, S.Kuriki, Y.Zhang, +Computations of the Expected Euler Characteristic for the Largest Eigenvalue of a Real Wishart Matrix, + + jmva +
  4. M.Harkonen, T.Sei, Y.Hirose, +Holonomic extended least angle regression, + arxiv:1809.08190 +
  5. S.Mano, +Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics, + +JSS Research Series in Statistics, 2018. +
  6. A.Kume, T.Sei, +On the exact maximum likelihood inference of Fisher–Bingham distributions using an adjusted holonomic gradient method, + doi (2018) +
  7. Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama, Nobuki Takayama, +Holonomic Gradient Method for Two Way Contingency Tables, + arxiv:1803.04170 +
  8. 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 +
  9. T.Koyama, +An integral formula for the powered sum of the independent, identically and normally distributed random variables, + arxiv:1706.03989 +
  10. 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 + +
  11. R.Vidunas, A.Takemura, +Differential relations for the largest root distribution +of complex non-central Wishart matrices, + arxiv:1609.01799 + +
  12. S.Mano, +The A-hypergeometric System Associated with the Rational Normal Curve and +Exchangeable Structures, + arxiv:1607.03569 + +
  13. M.Noro, +System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions, + ACM DL + +
  14. 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 + +
  15. T.Koyama, +Holonomic gradient method for the probability content of a simplex +region +with a multivariate normal distribution, + arxiv:1512.06564 + +
  16. N.Takayama, Holonomic Gradient Method (in Japanese, survey), + +hgm-dic.pdf + +
  17. N.Takayama, S.Kuriki, A.Takemura, +A-Hpergeometric Distributions and Newton Polytopes, + arxiv:1510.02269 + +
  18. G.Weyenberg, R.Yoshida, D.Howe, +Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace, + arxiv:1506.00142 + +
  19. 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 + +
  20. K.Ohara, N.Takayama, +Pfaffian Systems of A-Hypergeometric Systems II --- +Holonomic Gradient Method, + arxiv:1505.02947 + +
  21. T.Koyama, +The Annihilating Ideal of the Fisher Integral, + arxiv:1503.05261 + +
  22. T.Koyama, A.Takemura, +Holonomic gradient method for distribution function of a weighted sum +of noncentral chi-square random variables, + arxiv:1503.00378 + +
  23. Y.Goto, +Contiguity relations of Lauricella's F_D revisited, + arxiv:1412.3256 + +
  24. +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 + + +
  25. N.Marumo, T.Oaku, A.Takemura, +Properties of powers of functions satisfying second-order linear differential equations with applications to statistics, + arxiv:1405.4451 +
  26. J.Hayakawa, A.Takemura, Estimation of exponential-polynomial distribution by holonomic gradient descent arxiv:1403.7852 @@ -28,7 +142,9 @@ 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
  27. Intro @@ -51,7 +167,8 @@ Calculation of Orthant Probabilities by the Holonomic
  28. 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
  29. T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama, @@ -74,8 +191,8 @@ Journal of Multivariate Analysis, 116 (2013), 440--455
  30. T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral, Funkcialaj Ekvacioj 56 (2013), 51--61. - -jstage +DOI +
  31. Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara, @@ -84,8 +201,19 @@ 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. @@ -102,7 +230,13 @@ 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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