Abstract
Markov chains and hidden Markov models (HMMs) are particular types of PGMs that represent dynamic processes. After a brief introduction to Markov chains, this chapter focuses on hidden Markov models. The algorithms for solving the basic problems: evaluation, optimal sequence, and parameter learning are presented. The chapter concludes with a description of several extensions to the basic HMM, and two applications: the “PageRank” procedure used by Google and gesture recognition.
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Notes
- 1.
Do not confuse a state diagram, where a node represents each state—a specific value of a random variable—and the arcs transitions between states, with a graphical model diagram, where a node represents a random variable and the arcs represent probabilistic dependencies.
- 2.
This is a particular case of the Most Probable Explanation or MPE problem, which will be discussed in Chap. 7.
- 3.
If we have some domain knowledge this could provide a good initialization for the parameters; otherwise, we can set them to uniform probabilities.
- 4.
Hidden Markov models, including these extensions, are particular types of dynamic Bayesian networks, a more general model that is described in Chap. 9.
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Sucar, L.E. (2015). Hidden Markov Models. In: Probabilistic Graphical Models. Advances in Computer Vision and Pattern Recognition. Springer, London. https://doi.org/10.1007/978-1-4471-6699-3_5
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DOI: https://doi.org/10.1007/978-1-4471-6699-3_5
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