MAXIMUM-LIKELIHOOD-ESTIMATION VIA THE ECM ALGORITHM - A GENERAL FRAMEWORK

Two major reasons for the popularity of the EM algorithm are that its maximum step involves only complete-data maximum likelihood estimation , which is often computationally simple, and that its convergence is s table, with each iteration increasing the likelihood. When the associa ted complete-data maximum likelihood estimation itself is complicated, EM is less attractive because the M-step is computationally unattract ive. In many cases, however, complete-data maximum likelihood estimati on is relatively simple when conditional on some function of the param eters being estimated. We introduce a class of generalized EM algorith ms, which we call the ECM algorithm, for Expectation/Conditional Maxim ization (CM), that takes advantage of the simplicity of complete-data conditional maximum likelihood estimation by replacing a complicated M -step of EM with several computationally simpler CM-steps. We show tha t the ECM algorithm shares all the appealing convergence properties Of EM, such as always increasing the likelihood, and present several ill ustrative examples.