  Expectation Maximization (EM) is among the most popular algorithms for
estimating parameters of statistical models. However, EM, which is an iterative
algorithm based on the maximum likelihood principle, is generally only
guaranteed to find stationary points of the likelihood objective, and these
points may be far from any maximizer. This article addresses this disconnect
between the statistical principles behind EM and its algorithmic properties.
Specifically, it provides a global analysis of EM for specific models in which
the observations comprise an i.i.d. sample from a mixture of two Gaussians.
This is achieved by (i) studying the sequence of parameters from idealized
execution of EM in the infinite sample limit, and fully characterizing the
limit points of the sequence in terms of the initial parameters; and then (ii)
based on this convergence analysis, establishing statistical consistency (or
lack thereof) for the actual sequence of parameters produced by EM.
