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RCS file: /home/cvs/OpenXM/src/hgm/doc/ref-hgm.html,v
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retrieving revision 1.26
diff -u -p -r1.2 -r1.26
--- OpenXM/src/hgm/doc/ref-hgm.html 2014/03/24 06:58:31 1.2
+++ OpenXM/src/hgm/doc/ref-hgm.html 2018/07/06 06:01:51 1.26
@@ -3,7 +3,7 @@
References for HGM
-
+
@@ -12,7 +12,105 @@ the Holonomic Gradient Descent Method (HGD)
Papers and Tutorials
+- A.Kume, T.Sei,
+On the exact maximum likelihood inference of Fisher–Bingham distributions using an adjusted holonomic gradient method,
+ doi (2018)
+
- Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama, Nobuki Takayama,
+Holonomic Gradient Method for Two Way Contingency Tables,
+ arxiv:1803.04170
+
- 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
- T.Koyama,
+An integral formula for the powered sum of the independent, identically and normally distributed random variables,
+ arxiv:1706.03989
+
- 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 +118,9 @@ 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 +136,15 @@ 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 +167,8 @@ 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 +177,83 @@ 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.
-- hgm package for R for the step 3.
-
- 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
+
- Command line interfaces are in the folder OpenXM/src/hgm
+in the OpenXM source tree. See
+OpenXM distribution page .
+
- 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
+
+ - 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
- $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.1 2014/03/24 06:43:55 takayama Exp $
+ $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.25 2018/05/07 04:50:46 takayama Exp $