Hidden Markov models for labeled sequences

A hidden Markov model for labeled observations, called a class HMM, is introduced and a maximum likelihood method is developed for estimating the parameters of the model. Instead of training it to model the statistics of the training sequences it is trained to optimize recognition. It resembles MMI training, but is more general, and has MMI as a special case. The standard forward-backward procedure for estimating the model cannot be generalized directly, but an "incremental EM" method is proposed.