EM Algorithms

The EM algorithm is not a single algorithm, but a framework for the design of iterative likelihood maximization methods for parameter estimation. Any algorithm based on the EM framework we refer to as an “EM algorithm”. Because there is no inclusive theory that applies to all EM algorithms, the subject is a work in progress, and we find it appropriate to approach the subject through examples, each chosen to illustrate an important aspect of the subject. We begin on a positive note with the EM algorithm for finite mixtures of Poisson random variables, which arises in single-photon emission tomography (SPECT). In this case, for which we have a nearly complete theory of con-vergence, there emerges quite naturally a topology on the parameter space based on the cross-entropy, or Kullback-Leibler, distance between non-negative vectors. Because the distributions involve discrete probabilities, there is no difficulty in describing the EM framework. Our next example involves censored exponentially distributed data. No