Expectation–maximization algorithm

Summary

The expectation–maximization (EM) algorithm is an iterative method to compute maximum likelihood estimates when the data are incomplete or the model has latent variables. Each iteration has two steps. The expectation step averages the complete-data log-likelihood over the missing part, given the current parameter; the maximization step maximizes this average. Each iteration does not decrease the likelihood of the observed data. It is the standard method for fitting mixture models and hidden Markov models; Dempster, Laird and Rubin gave its general formulation in 1977.