Generalization of the Baum algorithm to rational objective functions

Abstract

The well-known Baum-Eagon inequality provides an effective iterative scheme for finding a local maximum for homogeneous polynomials with positive coefficients over a domain of probability values. However, in a large class of statistical problems, such as those arising in speech recognition based on hidden Markov models, it was found that estimation of parameters via some other criteria that use conditional likelihood, mutual information, or the recently introduced H-criteria can give better results than maximum-likelihood estimation. These problems require finding maxima for rational functions over domains of probability values, and an analog of the Baum-Eagon inequality for rational functions makes it possible to use an E-M (expectation-maximization) algorithm for maximizing these functions. The authors describe this extension.