Hmm Website Links For
Hidden
 

Information About

Hmm




State transitions in a hidden Markov model (example)

''x'' — hidden states

''y'' — observable outputs

''a'' — transition probabilities

''b'' — output probabilities]]
A hidden Markov model ('''HMM''') is a Statistical Model where the system being modeled is assumed to be a Markov Process with unknown parameters, and the challenge is to determine the hidden parameters from the Observable parameters. The extracted model parameters can then be used to perform further analysis, for example for Pattern Recognition applications.

In a regular Markov model, the state is directly visible to the observer, and therefore the state transition probabilities are the only parameters. In a ''hidden'' Markov model, the state is not directly visible, but variables influenced by the state are visible. Each state has a probability distribution over the possible output tokens. Thus the sequence of tokens generated by an HMM gives some information about the sequence of states.


EVOLUTION OF A MARKOV MODEL

The preceding diagram emphasizes the state transitions of a HMM. It is also useful to explicitly represent the evolution of the model over time, with the states at different times ''t''1 and ''t''2 represented by different variables, ''x''(''t''1) and ''x''(''t''2).





In this diagram, it is understood that the time slices (''x''(''t''), ''y''(''t'')) extend to previous and following times as needed. Typically the earliest slice is at time ''t''=0 or time ''t''=1.


USING MARKOV MODELS


There are 3 Canonical problems to solve with HMMs:
  • Given the model parameters, compute the probability of a particular output sequence. Solved by the Forward Algorithm .

  • Given the model parameters, find the most likely sequence of (hidden) states which could have generated a given output sequence. Solved by the Viterbi Algorithm .

  • Given an output sequence, find the most likely set of state transition and output probabilities. Solved by the Baum-Welch Algorithm .



A concrete example


''This example is further elaborated in Viterbi Algorithm page.''


Applications of hidden Markov models



HISTORY


Hidden Markov Models were first described in a series of statistical papers by Leonard E. Baum and other authors in the second half of the 1960s . One of the first applications of HMMs was Speech Recognition , starting in the mid- 1970s .Rabiner, p. 258

In the second half of the 1980s , HMMs began to be applied to the analysis of biological sequences, in particular DNA . Since then, they have become ubiquitous in the field of Bioinformatics .Durbin


SEE ALSO



NOTES



REFERENCES


  • '', 77 (2), p. 257–286, February 1989.

  • Richard Durbin, Sean R. Eddy, Anders Krogh, Graeme Mitchison. ''Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids''. Cambridge University Press, 1999. ISBN 0521629713.

  • Kristie Seymore, Andrew McCallum, and Roni Rosenfeld. ''Learning Hidden Markov Model Structure for Information Extraction''. AAAI 99 Workshop on Machine Learning for Information Extraction, 1999. ''(also at CiteSeer : {Link without Title} )''

  • http://www.comp.leeds.ac.uk/roger/HiddenMarkovModels/html_dev/main.html

  • J. Li , A. Najmi, R. M. Gray, Image classification by a two dimensional hidden Markov model, ''IEEE Transactions on Signal Processing'', 48(2):517-33, February 2000.



EXTERNAL LINKS