An exact lower bound on the misclassification probability

12/03/2017

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by   Iosif Pinelis, et al.

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A lower bound on the misclassification probability for a finite number of classes is obtained in terms of the total variation norms of the differences between the sub-distributions over the classes. This bound, which is shown to be exact in a certain rather strong sense, is based on an exact upper bound on the difference between the maximum and the mean of a finite set of real numbers, in terms of the sum of the absolute values of the pairwise differences between the numbers.