In the previous section, we discussed generating an observation sequence of a given HMM. But, in reality, most of the time we are not interested in generating the observation sequence, mostly because we don't know the parameters of the HMM to generate observations in the first place.
For a given HMM representation, in most of the applications, we are always trying to address the following three problems:
- Evaluation of the model: Given the parameters of the model and the observation sequence, estimating the probability of the sequence
- Predicting the optimal sequence: Given the parameters of the model and the observation sequence, estimating the most probable sequence of the state sequence that had produced these observations
- Parameter-learning: Given a sequence of observations, estimating the parameters of the HMM model that generated it
In this section...