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<title>References for HGM</title>

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Line 12 the Holonomic Gradient Descent Method (HGD) </h1>

Line 14 the Holonomic Gradient Descent Method (HGD) </h1>

<h2> Papers and Tutorials</h2>

<ol>

<li> Nobuki Takayama, Takaharu Yaguchi, Yi Zhang,

Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics,

<a href="https://arxiv.org/abs/2111.10947"> arxiv:2111.10947 </a>

<li> Shuhei Mano, Nobuki Takayama,

Algebraic algorithm for direct sampling from toric models,

<a href="https://arxiv.org/abs/2110.14992"> arxiv:2110.14992 </a>

<li> M.Adamer, A.Lorincz, A.L.Sattelberger, B.Sturmfels, Algebraic Analysis of Rotation Data

<a href="https://arxiv.org/abs/1912.00396"> arxiv: 1912.00396 </a>

<li>

Anna-Laura Sattelberger, Bernd Sturmfels,

D-Modules and Holonomic Functions

<a href="https://arxiv.org/abs/1910.01395"> arxiv:1910.01395 </a>

<li>

N.Takayama, L.Jiu, S.Kuriki, Y.Zhang,

Computations of the Expected Euler Characteristic for the Largest Eigenvalue of a Real Wishart Matrix,

<!--

<a href="https://arxiv.org/abs/1903.10099"> arxiv:1903.10099 </a> -->

<li> M.Harkonen, T.Sei, Y.Hirose,

Holonomic extended least angle regression,

<a href="https://arxiv.org/abs/1809.08190"> arxiv:1809.08190 </a>

<li> S.Mano,

Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics,

JSS Research Series in Statistics</a>, 2018.

<li> A.Kume, T.Sei,

On the exact maximum likelihood inference of Fisher–Bingham distributions using an adjusted holonomic gradient method,

<a href="https://doi.org/10.1007/s11222-017-9765-3"> doi </a> (2018)

<li> Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama, Nobuki Takayama,

Holonomic Gradient Method for Two Way Contingency Tables,

<a href="https://arxiv.org/abs/1803.04170"> arxiv:1803.04170 </a>

<li> 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),

<a href="https://arxiv.org/abs/1707.02564"> arxiv:1707.02564 </a>

<li> T.Koyama,

An integral formula for the powered sum of the independent, identically and normally distributed random variables,

<a href="https://arxiv.org/abs/1706.03989"> arxiv:1706.03989 </a>

<li> H.Hashiguchi, N.Takayama, A.Takemura,

Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability

by Holonomic Gradient Method,

Line 41 region

Line 83 region

with a multivariate normal distribution,

<a href="http://arxiv.org/abs/1512.06564"> arxiv:1512.06564 </a>

<li> N.Takayama, Holonomic Gradient Method (in Japanese, survey),

hgm-dic.pdf </a>

<li> N.Takayama, S.Kuriki, A.Takemura,

A-Hpergeometric Distributions and Newton Polytopes,

Line 241 maximal Likehood estimates for the Fisher-Bingham dist

Line 286 maximal Likehood estimates for the Fisher-Bingham dist

<li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>

</ol>

<pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.21 2016/11/03 23:05:22 takayama Exp $ </pre>

<pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.32 2020/08/24 23:24:27 takayama Exp $ </pre>

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