What does the area under the ROC curve (AUC) measure?

The area under the ROC curve (AUC) is a valuable metric for evaluating the performance of a binary classification model across different threshold values. Specifically, it quantifies how well the model distinguishes between the positive and negative classes. An AUC value of 1 indicates perfect classification, whereas a value of 0.5 suggests no discriminative power, akin to random guessing.

In this context, saying that the AUC measures the aggregate performance of a classifier at various threshold levels is accurate. By computing the AUC, you essentially capture the true positive rate against the false positive rate at multiple thresholds, summing up how well the classifier performs overall rather than at a single threshold point. This makes the AUC a robust measure, particularly in scenarios where class distribution may be imbalanced.

While the likelihood of correctly classifying a positive sample and the probability of achieving the correct prediction across thresholds both contribute to understanding a model's performance, they do not encapsulate the broader aggregate assessment that the AUC provides. Additionally, measuring the accuracy of the majority class predictions wouldn't be appropriate in this context, as it does not pertain to the model's ability to separate classes effectively across different decision thresholds.