What does the Area Under the Receiver Operating Characteristic curve (AUC-ROC) measure?

The Area Under the Receiver Operating Characteristic curve (AUC-ROC) is a powerful metric used to evaluate the performance of classification models, particularly in distinguishing between different classes. It measures the model's capability to distinguish between positive and negative classes across various threshold settings.

In the context of binary classification, the ROC curve plots the true positive rate against the false positive rate at different threshold levels. By calculating the area under this curve, the AUC provides a single scalar value that summarizes the model's performance. A higher AUC value indicates better discriminatory ability; specifically, it signifies that the model is more likely to rank a randomly chosen positive instance higher than a randomly chosen negative instance.

This distinction capability is particularly useful in scenarios where classes are imbalanced or where the cost of false positives and false negatives differs significantly. Therefore, when selecting a model, one can choose the one with a higher AUC to ensure better classification performance regardless of the chosen threshold.

The other options relate to aspects of model evaluation or characteristics that do not involve measuring the ability to distinguish between classes directly, making them less relevant in the context of AUC-ROC.