ABSTRACT
In their most basic form, EM algorithms provide a general method for finding local maxima of a likelihood function when we may conceive of some subset of the full data as having been unobserved in the experiment. These algorithms are the computational workhorses of maximum likelihood estimation in mixture models, which provide perhaps the best-known class of examples in which EM algorithms are effective; see also Chapter 2 for a comprehensive review. In adopting the “expansive” view in this chapter, we explain the EM mechanism without reference specifically to mixture models or even maximum likelihood. Indeed, we argue for a definition of EM that includes any algorithm based on the same basic principle that guarantees the algorithms’ success in their original framework. Then, returning to the topic of finite mixtures, we describe several algorithms we consider instances of EM that extend this framework, each one of them related to mixture models. In this way, we hope to both elucidate the workings of EM and demonstrate the broad applicability of these ideas, which we feel is a testament to the genius and simplicity of the EM scheme.
