Faragó, A.; Lugosi, G. An algorithm to find the global optimum of left-to-right hidden Markov model parameters. (English) Zbl 0693.60085 Probl. Control Inf. Theory 18, No. 6, 435-444 (1989). 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 Keywords:Hidden Markov Models; local optimum; speed of convergence; speech recognition PDFBibTeX XMLCite \textit{A. Faragó} and \textit{G. Lugosi}, Probl. Control Inf. Theory 18, No. 6, 435--444 (1989; Zbl 0693.60085)