Holonomic Decent Minimization Method for Restricted Maximum Likelihood Estimation

TL;DR

This paper extends the holonomic gradient descent method to handle constrained maximum likelihood estimation problems, enabling solutions for previously intractable models with parameter restrictions.

Contribution

The paper introduces a constrained version of the holonomic gradient descent method for MLE, addressing parameter restrictions in statistical models.

Findings

Successfully applied to constrained MLE problems

Enables solving intractable models with parameter constraints

Extends HGD to a new class of statistical estimation problems

Abstract

Recently, the school of Takemura and Takayama have developed a quite interesting minimization method called holonomic gradient descent method (HGD). It works by a mixed use of Pfaffian differential equation satisfied by an objective holonomic function and an iterative optimization method. They successfully applied the method to several maximum likelihood estimation (MLE) problems, which have been intractable in the past. On the other hand, in statistical models, it is not rare that parameters are constrained and therefore the MLE with constraints has been surely one of fundamental topics in statistics. In this paper we develop HGD with constraints for MLE .