Rabiner and Juang -- Tutorial on HMMs

Rabiner, L.; Juang, B., "An introduction to hidden Markov models," ASSP Magazine, IEEE [see also IEEE Signal Processing Magazine] , vol.3, no.1, pp. 4-16, Jan 1986

Summary

Rabiner and Huang give an overview of hidden Markov models and some of the things you can do with them.

HMMs are good for representing temporal sequences of data. The Markov property says that a current property of the system (such as an observation made on it), is affected by the previous observation. They work by holding information about a set of states, with transitions available between the states with different probabilities. Each state has a distribution of outputs. So if you were to use an HMM to generate a sequence of outputs (which is not how you use them, and doing something like this is a bad idea), you'd take a random walk at an initial state (chosen by the prior probabilities \pi of the HMM model). At the state you'd choose an output based on the state's output distribution, and then transition to a new state based on the transition probs from that state. Recurse until you output the desired number of symbols.

Some neat things to do with hidden Markov models:

1. Given an model and observation sequence, compute the probability of that sequence occurring from that model. Forward or Backward Algorithms


2. Given a model and observation sequence, compute the sequence of states through the model that has the highest probability of producing the output (optimal path). Viterbi Algorithm


3. Given a set of observations, determine the parameters of the model with maximal likelihood. Baum-Welch Algorithm

Discussion

Hidden Markov models are the gold standard for many machine learning classification tasks, including handwriting and speech recognition. While they have many potential powerful uses, they're still not a silver bullet for all tasks, especially if used incorrectly.

BibTeX

@ARTICLE{rabiner1986introHMMs
,title={An introduction to hidden {Markov} models}
,author={L. R. Rabiner and B. H. Juang}
,journal={IEEE ASSP Magazine}
,year={1986}
,month={Jan}
,volume={3}
,number={1}
,pages={4-16}
,ISSN={0740-7467}
}