A bit of background first maybe it clears things up a bit.
When talking about HMMs (Hidden Markov Models) there are generally 3 problems to be considered:
- Evaluation problem
- Evaluation problem answers the question: what is the probability that a particular sequence of symbols is produced by a particular model?
- For evaluation we use two algorithms: the forward algorithm or the backwards algorithm (DO NOT confuse them with the forward-backward algorithm).
- Decoding problem
- Decoding problem answers the question: Given a sequence of symbols (your observations) and a model, what is the most likely sequence of states that produced the sequence.
- For decoding we use the Viterbi algorithm.
- Training problem
- Training problem answers the question: Given a model structure and a set of sequences, find the model that best fits the data.
- For this problem we can use the following 3 algorithms:
- MLE (maximum likelihood estimation)
- Viterbi training(DO NOT confuse with Viterbi decoding)
- Baum Welch = forward-backward algorithm
To sum it up, you use the Viterbi algorithm for the decoding problem and Baum Welch/Forward-backward when you train your model on a set of sequences.
Baum Welch works in the following way.
For each sequence in the training set of sequences.
- Calculate forward probabilities with the forward algorithm
- Calculate backward probabilities with the backward algorithm
- Calculate the contributions of the current sequence to the transitions of the model, calculate the contributions of the current sequence to the emission probabilities of the model.
- Calculate the new model parameters (start probabilities, transition probabilities, emission probabilities)
- Calculate the new log likelihood of the model
- Stop when the change in log likelihood is smaller than a given threshold or when a maximum number of iterations is passed.
If you need a full description of the equations for Viterbi decoding and the training algorithm let me know and I can point you in the right direction.
