Bayesian Online Algorithms for Learning in Discrete Hidden Markov Models

We propose and analyze two different Bayesian online algorithms for learning in discrete Hidden Markov Models and compare their performance with the already known Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of generalization we draw learning curves in simplified situations for these algorithms and compare their performances. 1. Introduction. The unifying perspective of the Bayesian approach to machine learning allows the construction of efficient algorithms and sheds light on the characteristics they should have in order to attain such efficiency. In this paper we construct and characterize the performance of mean field online algorithms for discrete Hidden Markov Models (HMM) [5, 9] derived from approximations to a fully Bayesian algorithm. HMMs form a class of graphical models used to model the behavior of time series. They have a wide range of applications which includes speech recognition [9], DNA and protein analysis [3, 4] and econometrics [10]. Discrete HMMs are defined by an underlying Markov chain with hidden states q t , and B do not depend on time the HMM is said homogeneous, this is a simplifying assumption, which is not needed for online learning. The observed states y t of the HMM represent the observations of the time series, i.e., a time series from time t = 1 to t = T is represented by the observed sequence y