  We introduce the Prediction Advantage (PA), a novel performance measure for
prediction functions under any loss function (e.g., classification or
regression). The PA is defined as the performance advantage relative to the
Bayesian risk restricted to knowing only the distribution of the labels. We
derive the PA for well-known loss functions, including 0/1 loss, cross-entropy
loss, absolute loss, and squared loss. In the latter case, the PA is identical
to the well-known R-squared measure, widely used in statistics. The use of the
PA ensures meaningful quantification of prediction performance, which is not
guaranteed, for example, when dealing with noisy imbalanced classification
problems. We argue that among several known alternative performance measures,
PA is the best (and only) quantity ensuring meaningfulness for all noise and
imbalance levels.
