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The data for many classification problems, such as pattern and speechrecognition, follow mixture distributions. To quantify the optimum performancefor classification tasks, the Shannon mutual information is a naturalinformation-theoretic metric, as it is directly related to the probability oferror. The mutual information between mixture data and the class label does nothave an analytical expression, nor any efficient computational algorithms. Weintroduce a variational upper bound, a lower bound, and three estimators, allemploying pair-wise divergences between mixture components. We compare the newbounds and estimators with Monte Carlo stochastic sampling and bounds derivedfrom entropy bounds. To conclude, we evaluate the performance of the bounds andestimators through numerical simulations.

Bounds on mutual information of mixture data for classification tasks