Maximum Likelihood Estimation and Integration Algorithm for Modeling Complex Systems
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.
KeywordsMaximum Likelihood Estimate (MLE) Groebner Basis Holonomic Gradient Descent (HGD) Integration algorithm
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