Viterbi algorithm for real-time applications

Question

I know that given an HMM and an observation, Viterbi algorithm can guess the hidden states sequence that produce this observation. But what about the case you want to use it real-time? I mean finding the hidden states step by step. Every time an observation symbol is on the input, a hidden state is guessed, without knowing the whole observation sequence that's coming next. I want to use that for an audio application that is running in real time so the observation will be a sequence of values of an audio feature at each time frame.

Answer 1

If you are interested in predicting what the hidden state is at time T, when you see the observation O_T, then you have data O_1, ..., O_{T-1}, O_T. Now the most likely state is found with forward backwards, where the backward variable is simply 1, because we can't see into the future. In summary, we have P(We are in hidden state i at time T) = \alpha_T(i) / P(O_1, ..., O_T | \lambda), where P(O_1, ..., O_T| \lambda) = \sum_{i=1}^n \alpha_T(i). Then the max index over all i's of P(We are in hidden state i at time T) will be your hidden state.

Please refer to http://courses.media.mit.edu/2010fall/mas622j/ProblemSets/ps4/tutorial.pdf for the formal notation.

Please let me know if this is what you were after, or if you had something else in mind. If you just wanted to find the best sequence of states in realtime, just compute the alpha variables, no need to look into the future for that.