## Chapter 9. The EM Algorithm

The **Expectation Maximization** (**EM**) algorithm (Dempster, Laird, and Rubin 1977) is actually not really an algorithm, but a procedure for algorithms for the computation of the maximum likelihood estimators in data with missing values. The EM algorithm is typically used for problems where no closed-form solution is known; that is to say for the special kind of optimization problems where iteration is the only chance to get close to the optimal solution.

The EM algorithm is successfully used, especially in applications from data clustering in machine learning and computer vision, in natural language processing, in psychometrics, in price and managed risk of a portfolio and in medical image reconstruction, and it is the general procedure used to impute missing values in a data set.

All data scientists would benefit from knowing the functionality of the EM algorithm since it gives them a tool to solve many problems in practice where no exact solution exists.