A unified view for discriminative objective functions based on negative exponential of difference measure between strings

This paper presents a novel unified view of a wide variety of objective functions suitable for discriminative training applied to sequential pattern recognition problems, such as automatic speech recognition. Focusing on a central component of conventional objective functions, the sum of modified joint probabilities of observations and strings, the analysis generalizes these objective functions by weighting each term in the sum by an important function, the negative exponential of difference measure between strings. The interesting and valuable results of this investigation are highlighted in a comprehensive relationship chart that covers all of the common approaches (maximum mutual information, minimum classification error, minimum phone/word error), as well as corresponding novel generalizations and modifications of those approaches.