References for HGM

=================================================================== RCS file: /home/cvs/OpenXM/src/hgm/doc/ref-hgm.html,v retrieving revision 1.4 retrieving revision 1.13 diff -u -p -r1.4 -r1.13 --- OpenXM/src/hgm/doc/ref-hgm.html 2014/03/24 21:03:55 1.4 +++ OpenXM/src/hgm/doc/ref-hgm.html 2016/02/05 21:42:46 1.13 @@ -3,7 +3,7 @@ References for HGM - + @@ -12,6 +12,55 @@ the Holonomic Gradient Descent Method (HGD)

Papers and Tutorials

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 + +
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 + +
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 @@ -43,7 +92,8 @@ Calculation of Orthant Probabilities by the Holonomic
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 +116,8 @@ 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, @@ -76,29 +126,68 @@ 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

+Most 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 . +
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

@@ -106,6 +195,6 @@ tk_jack (for Jack polynomials) are for the steps 1 or

d-dimensional Fisher-Bingham System -

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