3. Hidden Markov models: the theory

We begin by presenting the principle of hidden Markov models, detailing the assumptions on which they are based and illustrating how they work with a few examples. Then, in keeping with tradition, we present hidden Markov models in terms of the "three problems" that need to be solved in order to use them in practice:

• calculating the probability of a sequence of observations;

• inference of the optimal state sequence given a sequence of observations ;

• learning the parameters of a hidden Markov model from a corpus of training sequences.

Finally, we mention a few particularly popular variants of hidden Markov models.