Recall (Sensitivity): Measuring Completeness

Recall, also known as Sensitivity or the True Positive Rate (TPR), addresses how completely a model identifies positive instances. Precision assesses the accuracy of the model's positive predictions; Recall tackles a different question: Out of all the actual positive instances that exist, how many did the model correctly identify?

Think about it like this: if there's something important you need to find (like identifying patients with a specific condition, or detecting faulty items on an assembly line), Recall measures how successful your model is at finding all of them. It measures the model's "completeness" in identifying positive cases.

Calculating Recall

Recall is calculated using the True Positives ($TP$) and False Negatives ($FN$) from the confusion matrix. Remember:

• True Positives ($TP$): The number of positive instances correctly classified as positive by the model.
• False Negatives ($FN$): The number of positive instances incorrectly classified as negative by the model (i.e., the positives the model missed).

The formula for Recall is:

$$\text{Recall} = \frac{TP}{TP + FN}$$

The denominator, $TP + FN$, represents the total number of actual positive instances in the dataset (those correctly identified plus those missed). Recall, therefore, gives you the proportion of these actual positives that your model successfully "recalled" or identified.

Interpreting Recall

Recall values range from 0 to 1 (or 0% to 100%).

• Recall = 1 (or 100%): The model identified every single positive instance correctly. There were no False Negatives. This is the ideal scenario in terms of completeness.
• Recall = 0 (or 0%): The model failed to identify any of the positive instances. All actual positives were classified as negative (all positives resulted in False Negatives).
• A value between 0 and 1 indicates the fraction of actual positives that were correctly identified. For example, a Recall of 0.75 means the model found 75% of all the true positive cases.

When is High Recall Important?

Prioritizing Recall is significant in situations where failing to identify a positive case (a False Negative) has serious consequences. Consider these examples:

1. Medical Diagnosis: In screening for a serious disease, missing a patient who actually has the disease (a False Negative) can be much more dangerous than incorrectly flagging a healthy patient for further testing (a False Positive). High Recall ensures that most people with the disease are identified.
2. Fraud Detection: Letting a fraudulent transaction slip through undetected (a False Negative) can be costly. A system optimized for high Recall aims to catch as many fraudulent activities as possible, even if it means sometimes flagging legitimate transactions for review (more False Positives).
3. Spam Filtering: While annoying, letting a legitimate email go to the spam folder (a False Positive) might be acceptable. However, missing an important spam email (e.g., a phishing attempt) and letting it reach the inbox (a False Negative) could be harmful. In security-focused spam detection, high Recall might be desired.

Recall vs. Precision

It's important to understand that Recall focuses on finding all the actual positives, whereas Precision focuses on ensuring that the instances the model predicts as positive are indeed positive. Often, increasing Recall can lead to a decrease in Precision, and vice versa. If you try to catch every possible positive instance (high Recall), you might end up incorrectly labeling more negative instances as positive (lowering Precision). This relationship is known as the Precision-Recall trade-off, which we'll discuss next.

In summary, Recall measures how effectively a model identifies all relevant instances within a dataset. It answers the question: "Of all the things we should have found, how many did we actually find?" It's a critical metric when the cost of missing a positive instance is high.