Quasi-Monte Carlo sampling to improve the efficiency of Monte Carlo EM

In this paper we investigate an efficient implementation of the Monte Carlo EM algorithm based on Quasi-Monte Carlo sampling. The Monte Carlo EM algorithm is a stochastic version of the deterministic EM (Expectation-Maximization) algorithm in which an intractable E-step is replaced by a Monte Carlo approximation. Quasi-Monte Carlo methods produce deterministic sequences of points that can significantly improve the accuracy of Monte Carlo approximations over purely random sampling. One drawback to deterministic Quasi-Monte Carlo methods is that it is generally difficult to determine the magnitude of the approximation error. However, in order to implement the Monte Carlo EM algorithm in an automated way, the ability to measure this error is fundamental. Recent developments of randomized Quasi-Monte Carlo methods can overcome this drawback. We investigate the implementation of an automated, datadriven Monte Carlo EM algorithm based on randomized Quasi-Monte Carlo methods. We apply this algorithm to a geostatistical model of online purchases and find that it can significantly decrease the total simulation effort, thus showing great potential for improving upon the efficiency of the classical Monte Carlo EM algorithm.