On learning parametric-output HMMs

Hidden Markov Models (HMM) are a standard tool in the modeling and analysis of time series with a wide variety of applications. When the number of hidden states is known, the standard method for estimating the HMM parameters from given observed data is the Baum-Welch algorithm [Baum et al., 1970]. The latter is known to suffer from two serious drawbacks: it 1 tends to converge (i) very slowly and (ii) only to a local maximum. Indeed, the problem of recovering the parameters of a general HMM is provably hard, in several distinct senses [Abe and Warmuth, 1992, Lyngsø and Pedersen, 2001, Terwijn, 2002]. In this paper we consider learning parametric-output HMMs with a finite and known number of hidden states, where the output from each hidden state follows a parametric distribution from a given family.