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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[ing] 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 θi 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
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