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We introduce the Prediction Advantage (PA), a novel performance measure forprediction functions under any loss function (e.g., classification orregression). The PA is defined as the performance advantage relative to theBayesian risk restricted to knowing only the distribution of the labels. Wederive the PA for well-known loss functions, including 0/1 loss, cross-entropyloss, absolute loss, and squared loss. In the latter case, the PA is identicalto the well-known R-squared measure, widely used in statistics. The use of thePA ensures meaningful quantification of prediction performance, which is notguaranteed, for example, when dealing with noisy imbalanced classificationproblems. We argue that among several known alternative performance measures,PA is the best (and only) quantity ensuring meaningfulness for all noise andimbalance levels.

The Prediction Advantage: A Universally Meaningful Performance Measure for Classification and Regression