Addendum to Hidden Markov Models
In the previous chapter, we discussed how it's possible to train an HMM using the forward-backward algorithm and we have seen that it is a particular application of the EM algorithm. The reader can now understand the internal dynamic in terms of E and M steps. In fact, the procedure starts with randomly initialized A and B matrices and proceeds in an alternating manner:
- E-Step:
- The estimation of the probability that the HMM is in the state i at time t and in the state j at time t + 1, given the observations and the current parameter estimations (A and B)
- The estimation of the probability that the HMM is in the state i at time t given the observations and the current parameter estimations (A and B)
- M-Step:
- Computing the new estimation for the transition probabilities aij (A) and for the emission probabilities bip (B)
The procedure is repeated until convergence is reached. Even if there's no explicit...