AUC-ROC

AUC-ROC is the area under the ROC curve, a metric that summarizes in a single number, between 0 and 1, a binary classifier's performance across all its possible decision thresholds. The ROC curve (receiver operating characteristic) plots the true positive rate against the false positive rate as that threshold is varied.

How it is interpreted

An AUC of 0.5 is equivalent to chance, and of 1.0, to perfect classification. It has a precise probabilistic reading: the AUC is the probability that the model assigns a higher score to a randomly chosen positive example than to a randomly chosen negative one. That is why it measures the ability to rank and discriminate—to separate positives from negatives—not the correctness of a specific prediction.

What the AUC does not tell you

Three limits are worth keeping in mind. First, the AUC measures discrimination, not calibration: two models with the same AUC can give very different probabilities, because the metric attends only to the order of the scores. Second, it sets no operating threshold: it summarizes performance across all cutoffs, but choosing the specific threshold is a separate decision that depends on the relative cost of false positives and false negatives. And third, with heavily imbalanced classes AUC-ROC can be optimistic, so it is usually complemented with the precision-recall curve (AUC-PR), focused on the minority class.

What it is used for

AUC-ROC is used to compare classifiers with a single threshold-independent figure and for model selection, often by averaging the AUC over the folds of a cross-validation.