AUC

AUC stands for Area Under the Curve. In statistics and machine learning, it most often refers to the Area Under the Receiver Operating Characteristic Curve (ROC AUC), a metric for evaluating binary classifiers. The term can also denote the area under other curves, such as precision-recall curves, or, in pharmacokinetics, a measure of drug exposure over time.

The ROC curve plots the true positive rate against the false positive rate across thresholds. The ROC AUC is the area under this curve, ranging from 0 to 1. A value near 0.5 indicates no discriminative ability; near 1 indicates perfect discrimination. Conceptually, it is the probability that a randomly chosen positive instance receives a higher score than a randomly chosen negative one, and it is invariant to monotonic transformations of the scores.

In multiclass problems, AUC can be extended with one-versus-rest schemes and averaged (micro or macro). AUC-ROC is relatively robust to class prevalence, but in highly imbalanced datasets the area under the precision-recall curve (AUC-PR) may be more informative for the positive class.

Limitations include that AUC summarizes ranking quality rather than probability calibration. Two models can have the same AUC but differ in calibration or risk stratification. Confidence intervals can be obtained by bootstrapping, and AUC is often supplemented by other metrics such as Brier score or AUC-PR for a fuller evaluation.