Acceleration of the EM algorithm via extrapolation methods: Review, comparison and new methods

EM-type algorithms are popular tools for modal estimation and the most widely used parameter estimation procedures in statistical modeling. However, they are often criticized for their slow convergence. Despite the appearance of numerous acceleration techniques along the last decades, their use has been limited because they are either difficult to implement or not general. In the present paper, a new generation of fast, general and simple maximum likelihood estimation (MLE) algorithms is presented. In these cyclic iterative algorithms, extrapolation techniques are integrated with the iterations in gradient-based MLE algorithms, with the objective of accelerating the convergence of the base iterations. Some new complementary strategies like cycling, squaring and alternating are added to that processes. The presented schemes generally exhibit either fast-linear or superlinear convergence. Numerical illustrations allow us to compare a selection of its variants and generally confirm that this category is extremely simple as well as fast.