The Three Fundamental Questions for HMMs
Given a model ?=(A, B, ?), how do we efficiently compute how likely a certain observation is, that is, P(O| ?)
Given the observation sequence O and a model ?, how do we choose a state sequence (X1, …, X T+1) that best explains the observations?
Given an observation sequence O, and a space of possible models found by varying the model parameters ? = (A, B, ?), how do we find the model that best explains the observed data?