1) Definition

Recall (also called Sensitivity or True Positive Rate) measures how many of the actual positives the model correctly identifies.

It answers:
“Of all the true positives in the dataset, how many did my model find?”

Formula:

$\text{Recall} = \frac{\text{True Positives (TP)}}{\text{True Positives (TP)} + \text{False Negatives (FN)}}$

  • TP (True Positives): Correctly predicted positives.
  • FN (False Negatives): Actual positives that the model missed.

2) Intuition

  • High recall → the model catches most of the true positives, but may include more false alarms.
  • Low recall → the model misses many true positives.

3) Example

Imagine a medical test for a disease:

  • Actual patients with disease = 100
  • Model predicts 80 correctly as positive (TP = 80)
  • Model misses 20 patients (FN = 20)

$\text{Recall} = \frac{80}{80 + 20} = 0.80$

Interpretation: The test detects 80% of the sick patients.

4) Contrast with Precision

  • Precision = Of predicted positives, how many are truly positive? (focus on false positives).
  • Recall = Of actual positives, how many were caught? (focus on false negatives).

Example:

  • A spam filter with high recall, low precision: flags almost all spam but also marks many good emails as spam.
  • A spam filter with high precision, low recall: flags only the most obvious spam, but misses a lot of subtle spam.

5) Why Recall is Important

  • In problems where missing positives is very costly:
    • Medical diagnosis (don’t miss sick patients).
    • Fraud detection (don’t miss fraudulent transactions).
    • Safety systems (don’t miss dangerous conditions).
  • Often optimized together with precision (via F1-score).

6) Related Metrics

  • F1-score: Harmonic mean of precision and recall.
    • $F1 = \frac{2 \cdot \text{Precision} \cdot \text{Recall}}{\text{Precision} + \text{Recall}}$
  • Specificity (True Negative Rate): Complement metric for negatives.
  • ROC-AUC & PR-AUC: Summarize trade-offs between recall and other metrics across thresholds.

Summary:
Recall = proportion of actual positives that the model correctly identifies.
It reflects the model’s ability to avoid false negatives and is crucial in high-risk domains where missing a positive case is more dangerous than raising a false alarm.