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Minimum phone error (MPE) is an objective function for discriminative training of acoustic models for speech recognition. Recently several different objective functions related to MPE have been proposed. In this paper we compare implementations of three of these to MPE on English and Arabic broadcast news. The techniques investigated are minimum phone frame error (MPFE), minimum divergence (MD), and a physical-state level version of minimum Bayes risk which we call s-MBR. In the case of MPFE we observe improvements over MPE. We propose that the smoothing constant used in MPE should be scaled according to the average value of the counts in the statistics obtained from these objective functions.
Povey et al. (Sun,) studied this question.