An Overview of ROC Curves
ROC (receiver operating characteristic) curves are graphs that show how well classification models perform at different thresholds. It does so by plotting the true positive rate against the false positive rate.
$$ True Positive Rate = frac{TP}{TP + FN}$$
$$False Positive Rate = frac{FP}{FP + TN}$$
The ROC curve plots true positive rate vs false positive rate for the range of possible classification thresholds.
Area under the ROC Curve
The AUC (Area under the ROC curve) provides a way of measuring performance for differing classification thresholds. Ultimately, it is what it sounds like: a measure of the area underneath the curve of an ROC. It ranks the probability that a random positive example exists closer to a 1.0 value on the ROC curve of a random negative value. If a model predicts correctly 100% of the time, it will have an AUC of 1.0. A model that predicts incorrectly every time will have an AUC of 0.