In ML, we maximize the probability of a given sequence of observations O, belonging to a given class, given the HMM λ of the class, with respect to the parameters of the model λ.
this probability is the total likelihood of the observations and can be expressed mathematically as: there is no known way to analytically solve for the model λ = {A, B, π} , which maximize the quantity L tot , where A is the transition probabilities, B is the observation probabilities, and π is the initial state distribution.