SMOOTH ONLINE LEARNING ALGORITHMS FOR HIDDEN MARKOV-MODELS

A simple learning algorithm for Hidden Markov Models (HMMs) is present ed together with a number of variations. Unlike other classical algori thms such as the Baum-Welch algorithm, the algorithms described are sm ooth and can be used on-line (after each example presentation) or in b atch mode, with or without the usual Viterbi most likely path approxim ation. The algorithms have simple expressions that result from using a normalized-exponential representation for the HMM parameters. All the algorithms presented are proved to be exact or approximate gradient o ptimization algorithms with respect to likelihood, log-likelihood, or cross-entropy functions, and as such are usually convergent. These alg orithms can also be casted in the more general EM (Expectation-Maximiz ation) framework where they can be viewed as exact or approximate GEM (Generalized Expectation-Maximization) algorithms. The mathematical pr operties of the algorithms are derived in the appendix.