Tutorial zum EM-Algorithmus (zweite Auflage)

The Maximum Likelihood Estimation (MLE) is a popular method for parameter estimation in both applied probability and statistics. However, MLE cannot solve the problem of incomplete or hidden data, as it is impossible to maximize the likelihood function based on hidden data. The Expectation-Maximization (EM) algorithm is a powerful mathematical tool for addressing this issue when there is a relationship between hidden and observed data. Such a relationship is specified by a mapping from hidden data to observed data or through a joint probability between them. The core idea of the EM algorithm is to maximize the expected value of the likelihood function over the observed data based on the hinting relationship, rather than directly maximizing the likelihood function of the hidden data. The pioneers of the EM algorithm have proven its convergence. As a result, the EM algorithm provides parameter estimators that are as good as those from MLE. This tutorial aims to provide explanations of the EM algorithm to help researchers understand it. Additionally, the second edition presents some applications of EM, such as mixture models, handling missing data, and learning hidden Markov models.