On the Convergence of the Em Algorithm

This paper obtains a derivation of region of convergence and asymptotic convergence rates for a specified complete data space by representing the E step in a Taylor series with remainder by the EM algorithm.

Abstract

The EM algorithm is a popular iterative method for finding the maximum likelihood estimate when the likelihood function is either non-analytical or its functional form is too difficult to maximize directly. In this paper we analyze the convergence properties of the EM algorithm. By representing the E step in a Taylor series with remainder we obtain a derivation of region of convergence and asymptotic convergence rates for a specified complete data space. These results can help one tailor the choice of complete data space so as to achieve an optimal tradeoff between ease of implementation and rapid convergence of the EM algorithm.