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Maximum mutual information (MMI) is a model selection criterion used forhidden Markov model (HMM) parameter estimation that was developed more thantwenty years ago as a discriminative alternative to the maximum likelihoodcriterion for HMM-based speech recognition. It has been shown in the speechrecognition literature that parameter estimation using the current MMIparadigm, lattice-based MMI, consistently outperforms maximum likelihoodestimation, but this is at the expense of undesirable convergence properties.In particular, recognition performance is sensitive to the number of times thatthe iterative MMI estimation algorithm, extended Baum-Welch, is performed. Infact, too many iterations of extended Baum-Welch will lead to degradedperformance, despite the fact that the MMI criterion improves at eachiteration. This phenomenon is at variance with the analogous behavior ofmaximum likelihood estimation -- at least for the HMMs used in speechrecognition -- and it has previously been attributed to `over fitting'. In thispaper, we present an analysis of lattice-based MMI that demonstrates, first ofall, that the asymptotic behavior of lattice-based MMI is much worse than waspreviously understood, i.e. it does not appear to converge at all, and, secondof all, that this is not due to `over fitting'. Instead, we demonstrate thatthe `over fitting' phenomenon is the result of standard methodology thatexacerbates the poor behavior of two key approximations in the lattice-basedMMI machinery. We also demonstrate that if we modify the standard methodologyto improve the validity of these approximations, then the convergenceproperties of lattice-based MMI become benign without sacrificing improvementsto recognition accuracy.

Approximations to the MMI criterion and their effect on lattice-based MMI