Is EM really necessary here? Examples where it seems simpler not to use EM

Abstract

If one is to judge by counts of citations of the fundamental paper (Dempster in JRSSB 39: 1–38, 1977), EM algorithms are a runaway success. But it is surprisingly easy to find published applications of EM that are unnecessary, in the sense that there are simpler methods available that will solve the relevant estimation problems. In particular, such problems can often be solved by the simple expedient of submitting the observed-data likelihood (or log-likelihood) to a general-purpose routine for unconstrained optimization. This can dispense with the need to derive and code (or modify) the E and M steps, a process which can sometimes be laborious or error-prone. Here, I discuss six such applications of EM in some detail, and in an appendix describe briefly some others that have already appeared in the literature. Whether these are atypical of applications of EM seems an open question, although one that may be difficult to answer; this question is of relevance to current practice, but may also be of historical interest. But it is clear that there are problems traditionally solved by EM (e.g. the fitting of finite mixtures of distributions) that can also be solved by other means. It is suggested that, before going to the effort of devising an EM algorithm to use on a new problem, the researcher should consider whether other methods (e.g. direct numerical maximization or an MM algorithm of some other kind) may be either simpler to implement or more efficient.