Franciso Vera
Department of Mathematical Sciences
Clemson University
Acceleration of the EM Algorithm in Mixture Models
Mixture models arise in a variety of real data situations. Parameters and
mixing proportions are typically estimated via maximum likelihood using the
EM algorithm. Several problems arise in the
fitting: the algorithm is extremely slow, the likelihood has several local
maxima and in certain circumstances could be unbounded, and the algorithm
fails when the parameters are in the boundary of the parameter space. Pilla
and Lindsay (2001) proposed variants of the EM algorithm and showed through
simulations these variants are dramatically quicker than classical EM, even
when the parameters are in the boundary of the parameter space. The choice
of inconsistent estimators as starting
values to get at the global maxima of the likelihood has also been studied
numerically (Biernacki et al, 2003). This work in progress tries to put some
of these ideas together. It considers theoretically why
Pilla and Lindsay variants are quicker and it also considers moments
estimators as starting values for the iteration.
Acknowledgements: Part of this effort is jointly with Ramani Pilla, Case
Western University.
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