I want to know - what are the differences between the forward-backward algorithm and the Viterbi algorithm for inference in hidden Markov models (HMM)?
A bit of background first maybe it clears things up a bit.
When talking about HMMs (Hiden Markov Models) there are generally 3 problems to be considered:
Baum Welch works in the following way
For each sequence in the training set of sequences
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.
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.
Forward-Backward gives marginal probability for each individual state, Viterbi gives probability of the most likely sequence of states. For instance if your HMM task is to predict sunny vs. rainy weather for each day, Forward Backward would tell you the probability of it being "sunny" for each day, Viterbi would give the most likely sequence of sunny/rainy days, and the probability of this sequence.