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Maximum Likelihood Estimation and Integration Algorithm for Modeling Complex Systems

  • Yoshinao ShirakiEmail author
Part of the Emergence, Complexity and Computation book series (ECC, volume 14)

Abstract

The holonomic gradient descent (HGD) method has been proposed as a means for calculating the maximum likelihood estimate (MLE), and its effectiveness has, in recent years, been reported within the statistics community. The purpose of HGD calculations is to reduce the calculation of the maximum likelihood estimate (MLE) of particular types of functions to calculating the minimum value of the holonomic function. As is well known, the maximum likelihood estimate (MLE) plays an important role in complex systems theory. In the complex systems community, however, little is known about the holonomic gradient descent (HGD) method. In this article, we introduce this method to the complex systems community and review the calculation mechanism of HGD.

Keywords

Maximum Likelihood Estimate (MLE) Groebner Basis Holonomic Gradient Descent (HGD) Integration algorithm 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Toho UniversityChibaJapan

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