References for HGM

=================================================================== RCS file: /home/cvs/OpenXM/src/hgm/doc/ref-hgm.html,v retrieving revision 1.3 retrieving revision 1.22 diff -u -p -r1.3 -r1.22 --- OpenXM/src/hgm/doc/ref-hgm.html 2014/03/24 07:54:51 1.3 +++ OpenXM/src/hgm/doc/ref-hgm.html 2016/11/03 23:19:18 1.22 @@ -3,7 +3,7 @@ References for HGM - + @@ -12,7 +12,92 @@ the Holonomic Gradient Descent Method (HGD)

Papers and Tutorials

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 + +
R.Vidunas, A.Takemura, +Differential relations for the largest root distribution +of complex non-central Wishart matrices, + arxiv:1609.01799 + +
S.Mano, +The A-hypergeometric System Associated with the Rational Normal Curve and +Exchangeable Structures, + arxiv:1607.03569 + +
M.Noro, +System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions, + ACM DL + +
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 + +
T.Koyama, +Holonomic gradient method for the probability content of a simplex +region +with a multivariate normal distribution, + arxiv:1512.06564 + + +
N.Takayama, S.Kuriki, A.Takemura, +A-Hpergeometric Distributions and Newton Polytopes, + arxiv:1510.02269 + +
G.Weyenberg, R.Yoshida, D.Howe, +Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace, + arxiv:1506.00142 + +
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 + +
K.Ohara, N.Takayama, +Pfaffian Systems of A-Hypergeometric Systems II --- +Holonomic Gradient Method, + arxiv:1505.02947 + +
T.Koyama, +The Annihilating Ideal of the Fisher Integral, + arxiv:1503.05261 +
T.Koyama, A.Takemura, +Holonomic gradient method for distribution function of a weighted sum +of noncentral chi-square random variables, + arxiv:1503.00378 + +
Y.Goto, +Contiguity relations of Lauricella's F_D revisited, + arxiv:1412.3256 + +
+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 + + +
N.Marumo, T.Oaku, A.Takemura, +Properties of powers of functions satisfying second-order linear differential equations with applications to statistics, + arxiv:1405.4451 + +
J.Hayakawa, A.Takemura, +Estimation of exponential-polynomial distribution by holonomic gradient descent + arxiv:1403.7852 + +
C.Siriteanu, A.Takemura, S.Kuriki, +MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method + arxiv:1403.3788 + +
T.Koyama, Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra, arxiv:1311.6905 @@ -20,7 +105,9 @@ 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
@@ -36,14 +123,15 @@ Calculating the Normalising Constant of the Bingham Di Statistics and Computing, 2013, DOI -
T.Koyama, +
T.Koyama, A.Takemura, Calculation of Orthant Probabilities by the Holonomic Gradient Method, arxiv:1211.6822
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
T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama, @@ -66,8 +154,8 @@ Journal of Multivariate Analysis, 116 (2013), 440--455
T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral, Funkcialaj Ekvacioj 56 (2013), 51--61. - -jstage +DOI +
Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara, @@ -76,36 +164,83 @@ Holonomic Gradient Descent and its Application to Fis Advances in Applied Mathematics 47 (2011), 639--658, DOI +

+Early papers related to HGM.
+

+H.Dwinwoodie, L.Matusevich, E. Mosteig, +Transform methods for the hypergeometric distribution, +Statistics and Computing 14 (2004), 287--297. +

+ + +

Three Steps of HGM

Find a holonomic system satisfied by the normalizing constant. +
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. -
Find an initial value vector for the holonomic system. +
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. -
Solve the holonomic system numerically. We use several methods +
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

+ +

+CRAN package hgm (for R). + +
+Some 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) are for the steps 1 or 2 and in the - asir-contrib +
3. Command line interfaces are in the folder OpenXM/src/hgm +in the OpenXM source tree. See +OpenXM distribution page . +
4. Experimental version of 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
+
```
  +
5. 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

d-dimensional Fisher-Bingham System

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