The Dynamic ECME Algorithm

The Expectation/Conditional Maximisation Either (ECME) algorithm has proven to be an effective way of accelerating the Expectation Maximisation (EM) algorithm for many problems. Recognising the limitation of using prefixed acceleration subspaces in ECME, we propose a Dynamic ECME (DECME) algorithm which allows the acceleration subspaces to be chosen dynamically. The simplest DECME implementation is what we call DECME-1, which uses the line determined by the two most recent estimates as the acceleration subspace. The investigation of DECME-1 leads to an efficient, simple, stable, and widely applicable DECME implementation, which uses two-dimensional acceleration subspaces and is referred to as DECME-2s. The fast convergence of DECME-2s is established by the theoretical result that in a small neighbourhood of the maximum likelihood estimate (MLE), it is equivalent to a conjugate direction method. The remarkable accelerating effect of DECME-2s and its variant is also demonstrated with multiple numerical examples.