29.6. Recall (Sensitivity or True Positive Rate)

Recall tells how many of the actual "yes" cases were correctly predicted.

Recall is a measure used to evaluate the performance of a classification model, specifically regarding its ability to identify positive cases. It answers the question: Of all the instances that were actually positive (yes), how many did the model correctly predict as positive? This is crucial for situations where missing a positive case can have serious consequences. The formula for calculating recall is: Recall = TP / (TP + FN), where TP stands for True Positives, and FN stands for False Negatives.

Think of a fire alarm system. The actual positive cases are the instances when there is indeed a fire (yes cases). Recall measures how many of those real fire situations are correctly detected by the alarm system. If the alarm fails to go off during an actual fire, that's a failure of recall, which can be dangerous.

Formula: 𝑇𝑃 Recall = 𝑇𝑃 +𝐹𝑁

The formula for recall is structured to provide a ratio of correctly identified positive cases to the total number of actual positive cases. In the formula, TP represents True Positives, which signifies the cases correctly predicted by the model as positive. FN represents False Negatives, which are the actual positive cases that the model incorrectly predicted as negative. Thus, this formula is crucial in determining the model's sensitivity or its ability to identify actual positive cases. For instance, if the model correctly identified 8 out of 10 actual positive cases, the recall would be calculated as 8 (TP) divided by (8 + 2) = 10 (TP + FN), resulting in a recall of 0.8 or 80%.

Imagine you are a teacher assessing your students' understanding of a subject. If you have 10 students who understood the material, but you only identify 8 of them as having understood, your recall reflects how well you have identified the students who truly understood (the ‘yes’ cases). If a student actually understood but you marked them incorrectly as having not understood, that’s a missed opportunity for feedback and improvement.

Use Case: Important when false negatives are dangerous, like in disease detection.

Recall is particularly vital in scenarios where the cost of a false negative is high. In medical diagnoses, for example, failing to identify a disease (false negative) can lead to severe consequences for the patient's health, potentially leading to death. Therefore, a system that prioritizes high recall would rather identify more positives (even at the expense of including some false positives) to ensure that as many actual cases as possible are detected and treated. This prioritization is essential in life-and-death contexts, where missing an actual positive case can have grave outcomes.

Consider a fire department responding to alarms. If an alarm does not go off when there is a fire (false negative), it could lead to significant damage and loss of life. Therefore, the fire department prioritizes systems that have high recall to ensure that any potential fire is detected early, even if that means occasionally responding to false alarms.

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