EM Algorithm And Its Acceleration

There are many applications that require the fitting of a parametric model to data in artificial intelligence statistics ,machine-learning, pattern-recognition.lt is often desired to estimate the maximum-likelihood or maximum-posterior likelihood . When all of the variables of the model are directly observable in the data, then it is relatively straightforward. But when some variable are hidden, maximun-likelihood estimation is much complicated.There are many methods for maximum-likelihood estimation from incomplete data. The Expectation-Maximization algorithm is a popular one ,which is also called EM algorithm and introduced by Dempster ,Laird & Rubin(1977)(DLR)in a presented paper in Royal Statistics Associate.Its advantage is simplicity and stability. Especially,the log-likelihood of the observed data is guaranteed to be non-decreasing at each iteration .They also defined Generalised EM algorithm(GEM ),which includes EM as a speial case ,and can be more computaionally efficient and guarantee the quality of EM algorithm.It is a general-purpose algorithm for maximum likelihood estimation in wide variety of situations best described as incomplete-data problem.The incomplete-data situations include not only evidently incomplete data situations,where there are missing data,truncated distributions,but also a whole variety of situations where the incompleteness of the data is not naural or evident. Due to the complicated computation of the maximum-likelihood estimation of the observed data, maximum likelihood estimation of the completed data will be simple ,after adding complmental parameter . In most cases ,it is a optimization algorithm and monotonly converge to the local maximum.The EM algorithm is not without limitation ,the most disadvantage is the slow speed of convergences many accelerations method are introduced to improved it. Each one has its own advantage and disadvantage.In this paper ,we present some acceleration methods and compare them experimentally.From the result of the experiment ,we argue that acceleration of the EM is possible ,but that which one is selected deponds on properties of the problem.