Optimal solution of a training problem in speech recognition

We take the view that the payoff correpsonding to different ways of training a speech recognizer is the probability that the recognizer will correctly recognize a randomly chosen word. In "A Decision Theoretic Formulation of a Training Problem in Speech Recognition" we posed the problem of choosing a speech recognizer as an optimization problem with the expected value of the above payoff as the objective function. This correspondence presents the optimal Bayes solution to this optimization problem by maximizing the expected payoff: conditionally on given training data decode the acoustic signal for a word as any word which maximizes the a posteriori expected joint probability of the word and the acoustic signal. Thus the probability estimator which is optimal for mean-squared error produces a decoder which happens to be optimal for recognition rate as well.