# AUC Area Under the ROC Curve (receiver operating characteristic)

An **ROC curve** (**receiver operating characteristic curve**) is a graph showing the performance of a classification model at all classification thresholds. This curve plots two parameters:

- True Positive Rate
- False Positive Rate

**True Positive Rate** (**TPR**) is a synonym for recall and is therefore defined as follows:

**False Positive Rate** (**FPR**) is defined as follows:

An ROC curve plots TPR vs. FPR at different classification thresholds. Lowering the classification threshold classifies more items as positive, thus increasing both False Positives and True Positives. The following figure shows a typical ROC curve.

**Figure 4. TP vs. FP rate at different classification thresholds.**

To compute the points in an ROC curve, we could evaluate a logistic regression model many times with different classification thresholds, but this would be inefficient. Fortunately, there’s an efficient, sorting-based algorithm that can provide this information for us, called AUC.

# AUC: Area Under the ROC Curve

**AUC** stands for “Area under the ROC Curve.” That is, AUC measures the entire two-dimensional area underneath the entire ROC curve (think integral calculus) from (0,0) to (1,1).

**Figure 5. AUC (Area under the ROC Curve).**