ABSTRACT
This chapter explains the expectation-maximization (EM) mechanism without reference specifically to mixture models or even maximum likelihood. It argues that a definition of EM that includes any algorithm based on the same basic principle that guarantees the algorithms’ success in their original framework. The chapter describes several algorithms the authors consider instances of EM that extend the framework, each one of them related to mixture models. It explores the workings of EM and demonstrates the broad applicability of these ideas, which the authors feel is a testament to the genius and simplicity of the EM scheme. Mixture models provide a wide variety of observed- and missing-data examples well suited to EM algorithms. In particular, the linear rate of convergence that characterizes EM algorithms may be exploited to engineer a stopping criterion that strives to ensure numerical accuracy in parameter estimates rather than reacting to slow progress of the algorithm.
