Specificity (True Negative Rate)¶
Formula¶
\[
\mathrm{Specificity}=\frac{TN}{TN+FP}
\]
Parameters¶
- \(TN\): true negatives
- \(FP\): false positives
What it means¶
Specificity measures how well a classifier correctly rejects negative cases.
What it's used for¶
- Medical screening and fraud detection when false positives are costly.
- ROC analysis (specificity = 1 - FPR).
Key properties¶
- Range is \([0,1]\).
- Threshold-dependent metric.
Common gotchas¶
- High specificity can come with low sensitivity if threshold is too strict.
- Undefined if there are no actual negatives.
Example¶
A spam filter with low false positives has high specificity on legitimate email.
How to Compute (Pseudocode)¶
Input: confusion-matrix counts
Output: specificity
compute the required numerator/denominator from TP, FP, FN, TN
if denominator == 0:
return undefined (or use a task-specific convention)
return numerator / denominator
Complexity¶
- Time: \(O(1)\) once confusion-matrix counts are available
- Space: \(O(1)\)
- Assumptions: Binary classification formula shown; computing the confusion matrix itself is typically \(O(n)\)