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Theory and Use of the EM Algorithm introduces the expectation-maximization (EM) algorithm and provides an intuitive and mathematically rigorous understanding of this method. It describes in detail two of the most popular applications of EM: estimating Gaussian mixture models (GMMs), and estimating hidden Markov models (HMMs). It also covers the use of EM for learning an optimal mixture of fixed models, for estimating the parameters of a compound Dirichlet distribution, and for disentangling superimposed signals. It discusses problems that arise in practice with EM, and variants of the algorithm that help deal with these challenges. Theory and Use of the EM Algorithm is designed to be useful to both the EM novice and the experienced EM user looking to better understand the method and its use.