Expectation–maximization algorithm
Variants

A number of methods have been proposed to accelerate the sometimes slow convergence of the EM algorithm, such as those using conjugate gradient and modified Newton's methods (Newton–Raphson). Also, EM can be used with constrained estimation methods.

Parameter-expanded expectation maximization (PX-EM) algorithm often provides speed up by "us a `covariance adjustment' to correct the analysis of the M step, capitalising on extra information captured in the imputed complete data".

Expectation conditional maximization (ECM) replaces each M step with a sequence of conditional maximization (CM) steps in which each parameter θ is maximized individually, conditionally on the other parameters remaining fixed. Itself can be extended into the Expectation conditional maximization either (ECME) algorithm.

This idea is further extended in generalized expectation maximization (GEM) algorithm, in which is sought only an increase in the objective function F for both the E step and M step as described in the As a maximization–maximization procedure section. GEM is further developed in a distributed environment and shows promising results.

It is also possible to consider the EM algorithm as a subclass of the MM (Majorize/Minimize or Minorize/Maximize, depending on context) algorithm, and therefore use any machinery developed in the more general case.
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