Noisy Hidden Markov Models for Speech Recognition

We show that noise can speed training in hidden Markov models (HMMs). The new Noisy ExpectationMaximization (NEM) algorithm shows how to inject noise when learning the maximum-likelihood estimate of the HMM parameters because the underlying Baum-Welch training algorithm is a special case of the Expectation-Maximization (EM) algorithm. The NEM theorem gives a sufficient condition for such an average noise boost. The condition is a simple quadratic constraint on the noise when the HMM uses a Gaussian mixture model at each state. Simulations show that a noisy HMM converges faster than a noiseless HMM on the TIMIT data set.