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Variational sampling approaches to word confusability

In speech recognition it is often useful to determine how confusable two words are. For speech models this comes down to computing the Bayes error between two HMMs. This problem is analytically and numerically intractable. A common alternative, that is numerically approachable, uses the KL divergence in place of the Bayes error. We present new approaches to approximating the KL divergence, that combine variational methods with importance sampling. The Bhattacharyya distance - a closer cousin of the Bayes error - turns out to be even more amenable to our approach. Our experiments demonstrate an improvement of orders of magnitude in accuracy over conventional methods.