Sensitivity (True Positive Rate)¶
Formula¶
\[
\mathrm{Sensitivity}=\frac{TP}{TP+FN}
\]
Parameters¶
- \(TP\): true positives
- \(FN\): false negatives
What it means¶
Sensitivity measures how well a classifier captures actual positive cases.
What it's used for¶
- Detection tasks where misses are costly (disease, fraud, safety alerts).
- ROC analysis (same as recall/TPR).
Key properties¶
- Equivalent to recall in binary classification.
- Threshold-dependent metric.
Common gotchas¶
- High sensitivity may increase false positives.
- Undefined if there are no actual positives.
Example¶
A disease screening test tuned to catch nearly all true cases aims for high sensitivity.
How to Compute (Pseudocode)¶
Input: confusion-matrix counts
Output: sensitivity
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 \(O(n)\)