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An algorithm to find the global optimum of left-to-right hidden Markov model parameters. (English) Zbl 0693.60085

Summary: A central problem concerning the so-called Hidden Markov Models (HMM) is the following: given a finite observation sequence, find a HMM (with a restricted number of states), which should produce the observation sequence with the highest possible probability. However, the existing algorithms, such as the Baum-Welch (forward-backward) re-estimation procedure, converge only to a local optimum at an uncertain speed of convergence.
We show that with a slight and practically justifiable modification of the objective function the situation becomes much better: there exists a fast non-iterative algorithm to find the global optimum for the class of left-to-right models which play a central role in some applications, such as speech recognition.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
81P20 Stochastic mechanics (including stochastic electrodynamics)
60J99 Markov processes
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