Hidden Markov model

A hidden Markov model (HMM) is a statistical model where the system being modelled is assumed to be a Markov process with unknown parameters, and the challenge is to determine the hidden parameters of the Markov model based on this assumption.

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. A hidden Markov model adds outputs: each state has a probability distribution over the possible output tokens. Therefore, looking at a sequence of tokens generated by an HMM does not directly indicate the sequence of states.

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[?].

Applications of hidden Markov models:

• speech recognition
• natural language understanding
• genomics
• and many more...

See also:

• Bayesian inference
• Viterbi algorithm
• Parameter estimation[?]

External links

• http://www.ai.mit.edu/~murphyk/Software/HMM/hmm
• A simple mathematical presentation of HMMs (http://www.cs.brown.edu/research/ai/dynamics/tutorial/Documents/HiddenMarkovModels)
• http://www.zaik.uni-koeln.de/~hmm/ghmm/
• Learning Hidden Markov Model Structure for Information Extraction (http://citeseer.nj.nec.com/seymore99learning)