Pattern Recognition, 4th Edition

9.7. HMM with State Duration Modeling

Hidden Markov modeling, as we have approached it so far, falls short of expectations in many cases in practice. Experimental evidence has identified a serious shortcoming associated with the use of the self-transition probabilities, P(i|i), as parameters in the standard HMMs. This is related to the exponential modeling of the state duration probability, Pⁱ(d), that such a modeling implies, where d is the successive number of times the model remains in state i. Indeed, given P(i|i) the probability of a path leaving current state i is equal to 1 — P(i|i). Hence, the probability of being in state i for d successive instants (i.e., d – 1 self-transitions, and emission of d consecutive observations from state ...