The Prediction Advantage: A Universally Meaningful Performance Measure for Classification and Regression
This provides a universally meaningful performance measure for researchers and practitioners in machine learning and statistics, addressing issues in noisy imbalanced problems, though it is incremental as it builds on existing concepts like R-squared.
The paper tackles the problem of evaluating prediction performance in classification and regression by introducing the Prediction Advantage (PA), a measure that quantifies advantage relative to Bayesian risk based on label distribution, ensuring meaningfulness across all noise and imbalance levels.
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.