Recall¶

Formula¶

\[ \operatorname{Recall} = \frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}} \]

Parameters¶

\(\mathrm{TP}\): true positives
\(\mathrm{FN}\): false negatives

What it means¶

Of the actual positives, how many are correctly identified.

What it's used for¶

Estimating how many true positives were found.
Tuning thresholds when false negatives are costly.

Key properties¶

Sensitive to false negatives
Trades off with precision via the decision threshold

Common gotchas¶

Undefined if \(\mathrm{TP}+\mathrm{FN}=0\) (no positives in ground truth).
Also called sensitivity or true positive rate.

Example¶

If \(\mathrm{TP}=30\) and \(\mathrm{FN}=5\), \(\mathrm{Recall}=30/(30+5)=0.857\).

How to Compute (Pseudocode)¶

Input: confusion-matrix counts
Output: recall

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 \(O(n)\)