Recall

What Is Recall?

Recall is an evaluation metric used in classification. It measures how many actual positives were found by the model.

Formula

Recall = True Positives / All Actual Positives

Out of all examples that were truly positive, how many did the model catch?

Recall focuses on the model's ability to find positive cases.

Why Recall Matters

Recall matters when missing a positive case is costly or dangerous. A false negative happens when the model predicts negative, but the true answer is positive.

Medical Diagnosis Example
  • Prediction: No Disease
  • True Label: Disease Present
  • Problem: A sick patient may not receive follow-up care.

High recall is important because the model should find as many true cases as possible.

Actual Positives

Actual positives are all examples that truly belong to the positive class. They include true positives and false negatives.

Disease Dataset
  • Actual Positive Cases: 100 patients
  • Found by Model: 80 patients
  • Missed by Model: 20 patients
  • True Positives: 80, False Negatives: 20
  • Recall = 80 / 100 = 80%

True Positives

A true positive happens when the model predicts positive and the true label is also positive. These are positive cases the model successfully found.

Disease Detection Example
  • Prediction: Disease Present
  • True Label: Disease Present
  • Result: True Positive

False Negatives

A false negative happens when the model predicts negative, but the true label is positive. These are actual positive cases the model missed.

Disease Detection Example
  • Prediction: No Disease
  • True Label: Disease Present
  • Result: False Negative

Recall Formula

Recall is calculated using true positives and false negatives.

Formula

Recall = True Positives / (True Positives + False Negatives)

Short Form: Recall = TP / (TP + FN)

The denominator means: All actual positives.

Recall Calculation Example

Imagine a model is trying to identify positive cases in a dataset.

Calculation
  • True Positives: 70
  • False Negatives: 30
  • Recall = 70 / (70 + 30) = 70 / 100 = 70%

The model found 70% of the actual positive cases.

High Recall

High recall means the model finds most actual positives. It is useful when missing positives is dangerous.

Disease Model Example
  • Actual Disease Cases: 100
  • Found by Model: 95
  • Missed: 5
  • Recall: 95%

Low Recall

Low recall means the model misses many actual positives. It can be risky when the positive class is important.

Fraud Detection Example
  • Actual Fraud Transactions: 100
  • Found by Model: 40
  • Missed: 60
  • Recall: 40%

Recall in Medical Diagnosis

In medical diagnosis, recall is often very important because missed cases can delay care.

Example
  • Actual Disease Cases: 200
  • Detected by Model: 180
  • Missed by Model: 20
  • Recall: 90%

A high recall means the model finds most patients who may need care.

Recall in Fraud Detection

In fraud detection, recall measures how many actual fraud cases were found. Higher recall helps reduce missed fraud.

Example
  • Actual Fraud Cases: 500
  • Fraud Cases Found: 350
  • Fraud Cases Missed: 150
  • Recall: 70%

Recall in Safety Systems

Recall is important in safety systems because missing a dangerous event can be harmful.

Example
  • Actual Dangerous Objects: 50
  • Detected: 48
  • Missed: 2
  • Recall: 96%

Recall in Spam Detection

In spam detection, recall measures how many actual spam emails were caught. High recall means most spam emails are caught, but precision should also be checked.

Example
  • Actual Spam Emails: 1,000
  • Caught by Model: 900
  • Missed Spam Emails: 100
  • Recall: 90%

Recall vs Accuracy

Accuracy measures overall correctness. Recall focuses only on actual positives.

Accuracy Asks

Out of all predictions, how many were correct?

Recall Asks

Out of all actual positives, how many did the model find?

A model can have high accuracy but low recall when positives are rare.

Recall vs Precision

Recall and precision measure different parts of performance. Recall focuses on avoiding false negatives, while precision focuses on avoiding false positives.

Recall

Out of all actual positives, how many were found?

Disease: How many sick patients were found?

Precision

Out of all predicted positives, how many were actually positive?

Disease: How many predicted sick patients were actually sick?

Recall and Precision Tradeoff

Recall and precision often have a tradeoff. Increasing recall can lower precision, and increasing precision can lower recall.

Lower Threshold
  • More cases predicted positive
  • Recall may increase
  • Precision may decrease
Higher Threshold
  • Fewer cases predicted positive
  • Precision may increase
  • Recall may decrease

When Recall Is More Important

Recall is more important when false negatives are costly.

Recall Is Important For
  • Disease detection — missing a disease can delay care
  • Fraud detection — missing fraud can cause financial loss
  • Safety monitoring — missing a dangerous event can cause harm
  • Cybersecurity — missing an attack can expose systems
  • Searching for critical documents — missing results can be costly

Main goal: Find as many actual positives as possible.

When Precision May Be More Important

Precision may be more important when false positives are more costly.

Precision May Matter More For
  • Spam filtering — normal emails marked as spam cause missed communication
  • Fraud alerts that block users — normal transactions blocked frustrate users
  • Hiring screening — weak candidates incorrectly recommended waste review time

Main goal: Positive predictions should be trustworthy.

Recall in a Confusion Matrix

A confusion matrix shows true positives, false positives, true negatives, and false negatives. Recall uses true positives and false negatives.

Recall Uses
  • True Positives
  • False Negatives

Recall does not directly use True Negatives or False Positives.

Formula: Recall = TP / (TP + FN)

Confusion Matrix Example

This example shows how recall is calculated from a confusion matrix.

Disease Detection
  • True Positives: 45
  • False Positives: 15
  • True Negatives: 30
  • False Negatives: 10
  • Recall = 45 / (45 + 10) = 45 / 55 = 82%

The model found 82% of the actual disease cases.

Perfect Recall

Perfect recall means the model found every actual positive. However, it does not always mean the model is perfect.

Example
  • True Positives: 100
  • False Negatives: 0
  • Recall = 100 / (100 + 0) = 100%

The model missed no positive cases, but may still make many false positive predictions.

Recall Can Be Misleading Alone

Recall alone does not tell the full story.

Example

A model predicts every transaction as fraud.

  • Actual Fraud Cases: 100
  • Fraud Cases Found: 100
  • Recall: 100%

Problem: The model may also incorrectly flag thousands of normal transactions. This is why recall should often be considered with precision.

Recall and F1 Score

F1 score combines precision and recall into one balanced metric.

Fraud Detection
  • Recall — How many fraud cases were found?
  • Precision — How many fraud alerts were truly fraud?
  • F1 Score — Balances both precision and recall.

Recall in Imbalanced Datasets

Recall is often important in imbalanced datasets, especially when the positive class is rare but important.

Fraud Is Rare

Most transactions are normal. Accuracy can be high while missing most fraud.

Recall helps answer: Out of all fraud cases, how many did the model catch?

Improving Recall

Improving recall usually means helping the model find more actual positives.

Ways to Improve Recall
  • Lower the classification threshold
  • Collect more positive examples
  • Balance the dataset
  • Improve feature quality
  • Fix incorrect labels
  • Use a better model for the task
  • Reduce false negatives
  • Tune the model carefully
  • Use data augmentation when appropriate

Classification Threshold

Many classification models output probabilities. A threshold decides when the model predicts positive.

Example
  • Disease Probability: 0.42
  • Default Threshold: 0.50
  • To improve recall: Lower the threshold to 0.30

A lower threshold makes the model flag more cases as positive, which may catch more actual positives.

Threshold Tradeoff

Lowering the threshold can improve recall, but it may reduce precision.

Lower Threshold
  • More positive predictions
  • More actual positives found
  • More false positives
Higher Threshold
  • Fewer positive predictions
  • Fewer false positives
  • More missed positives

Real-World Example: Disease Screening

A disease screening model should often have high recall because missing a real disease case may be harmful.

Disease Screening
  • False Negative — Patient has disease, but model says no disease
  • High Recall — Most actual disease cases are found
  • Possible Tradeoff — More people without the disease may be flagged for follow-up

Real-World Example: Fraud Detection

A fraud detection model with low recall may miss many fraudulent transactions.

Fraud Detection
  • False Negative — Fraud transaction marked as normal
  • High Recall — More fraud transactions are caught
  • Possible Tradeoff — Some normal transactions may be incorrectly flagged

Real-World Example: Search and Information Retrieval

Recall can measure how many relevant documents were found. High recall is useful when missing relevant information is costly.

Example
  • Relevant Documents: 100
  • Documents Found: 75
  • Recall: 75%

The system found 75% of relevant documents.

Common Mistakes

Common Mistakes
  • Confusing recall with accuracy
  • Confusing recall with precision
  • Looking at recall alone
  • Ignoring false positives
  • Ignoring the classification threshold
  • Assuming high recall means the model is always good
  • Ignoring the real-world cost of mistakes
  • Ignoring performance across different groups

Summary

Key Takeaways
  • Recall measures how many actual positives were found.
  • Recall focuses on actual positive cases.
  • Recall uses true positives and false negatives.
  • Recall formula is TP / (TP + FN).
  • High recall means fewer false negatives.
  • Recall is useful when false negatives are costly.
  • Recall is different from accuracy and precision.
  • Recall alone can be misleading.
  • Recall is often used with precision and F1 score.
  • Changing the classification threshold can affect recall.

Practice Prompt

A disease detection model is tested on 120 patients who actually have a disease. The model correctly identifies 90 of them and misses 30.

Calculate the recall. Then explain what the recall score means and why false negatives matter in this example.

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