What does a ROC curve illustrate?

A ROC (Receiver Operating Characteristic) curve is a graphical representation that illustrates the performance of a binary classifier. It plots the true positive rate (sensitivity) against the false positive rate (1 - specificity) at various threshold settings. This curve provides insights into how well a classifier distinguishes between the positive and negative classes.

The area under the ROC curve (AUC) is often used as a summary measure to quantify the overall ability of the model to discriminate between the two classes. A model with an AUC of 0.5 suggests no discrimination capability (similar to random guessing), while an AUC of 1 indicates perfect discrimination.

Understanding the ROC curve is essential for evaluating classifiers, especially in imbalanced datasets or when the cost of false positives and false negatives differs.