Forward Algorithm

3. Summary

Our aim is to find the probability of a sequence of observations given a HMM - (Pr (observations | ).

We reduce the complexity of calculating this probability by first calculating partial probabilities ('s). These represent the probability of getting to a particular state, s, at time t.

We then see that at time t = 1, the partial probabilities are calculated using the initial probabilities (from the vector) and Pr(observation | state) (from the confusion matrix); also, the partial probabilities at time t (> 1) can be calculated using the partial probabilities at time t-1.

This definition of the problem is recursive, and the probability of the observation sequence is found by calculating the partial probabilities at time t = 1, 2, ..., T, and adding all 's at t = T.

Notice that computing the probability in this way is far less expensive than calculating the probabilities for all sequences and adding them.