False Positive Rate - Aetherwisp

The False Positive Rate (FPR) is a performance index that states how many negative cases are wrongly classified as positive. Formally:

f_\text{FPR}(\{ y^{i},\hat{y}^{i} \}_{i})=\frac{\sum_{i=1}^{N}\mathrm{I}(y^{i}=\text{neg or }y^{i}\neq \hat{y}^{i})}{\sum_{i=1}^{N} \mathrm{I}(y^{i}=\text{neg})}

FPR is defined between 0 and 1 (a percentage). If there are no positives, it is undefined (divides by zero). FPR is best when its lowest. It's commonly provided alongside the False Negative Rate.

A more convenient notation is

\text{FPR}=\frac{\text{FP}}{\text{N}}

where $\text{FP}$ is the number of false positives and $\text{N}$ is the number of negatives. This assumes the presence of a real and predicted set $\{ y^{i},\hat{y}^{i} \}$ even if not written. Counting false positives needs both $y^{i}$ and $\hat{y}^{i}$ , whereas counting negatives only need $y^{i}$ .

A sibling quantity is the True Positive Rate, which is the count of correctly classified positives. It is the complement of FPR:

\text{TPR}=1-\text{FPR}

Like FPR, TPR is defined on $[0,1]$ . You want TPR to be as close to 1 as possible. TPR is also called sensitivity, because it's measures how much a classifier is sensitive to errors and capable of discerning between a true positive and false positive. This term is more common in diagnostic tests.