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The EM Algorithm as a Lower Bound Optimization Technique

The Expectation-Maximization (EM) algorithm is an iterative optimization technique that seeks to find the maximum likelihood parameter estimates in problems where some of the data is missing or hidden, or in problems that can be posed in a similar form, such as mixture model parameter estimation. The EM algorithm can be viewed in many different ways, one of the most insightful being in terms of lower bound maximization which better illustrates its underlying principles. There are several very good references discussing the EM algorithm in greater generality. The purpose of report is to present the EM algorithm in a more self-contained way from a lower bounding viewpoint, and show how it can be used used to find the parameters of a mixture of densities.