The (alpha)-EM algorithm: surrogate likelihood maximization using (alpha)logarithmic information measures

A new likelihood maximization algorithm called the (alpha)-EM algorithm ((alpha)expectation-maximization algorithm) is presented. This algorithm outperforms the traditional or logarithmic EM algorithm in terms of convergence speed for an appropriate range of the design parameter (alpha). The log-EM algorithm is a special case corresponding to (alpha)=-1. The main idea behind the (alpha)-EM algorithm is to search for an effective surrogate function or a minorizer for the maximization of the observed dataʹs likelihood ratio. The surrogate function adopted in this paper is based upon the (alpha)-logarithm which is related to the convex divergence. The convergence speed of the (alpha)-EM algorithm is theoretically analyzed through (alpha)-dependent update matrices and illustrated by numerical simulations. Finally, general guidelines for using the (alpha)logarithmic methods are given. The choice of alternative surrogate functions is also discussed.