30.3.3. Recall (Sensitivity or True Positive Rate)

Recall = TP / (TP + FN) It tells us how many actual positives were correctly predicted.

Recall, also known as sensitivity or the true positive rate, is a metric that measures the ability of a classification model to correctly identify all relevant instances within the data. Specifically, it looks at the proportion of actual positives that were correctly predicted as positive. It is calculated by dividing the number of true positives (TP) by the sum of true positives and false negatives (TP + FN). This means that if the model predicts a positive class correctly, it counts towards the recall, but if it fails to predict a positive instance and predicts it as negative, it counts against the recall.

Imagine a doctor trying to diagnose a disease. The doctor correctly identifies patients who have the disease most of the time, but not always. Recall would represent how many of the actual patients with the disease were correctly diagnosed by the doctor. If there are 10 actual patients with the disease and the doctor correctly identifies 8 of them, the recall would be 8/10 = 0.8 or 80%. A high recall means that the doctor is good at catching most patients with the disease.

Recall is especially important in situations where the cost of missing a positive instance is high.

Recall is crucial in contexts where failing to identify a positive case can have severe consequences. For example, in medical diagnoses, failing to detect a disease can lead to serious health risks for patients. High recall ensures that most patients who have the condition are identified and treated adequately, thus reducing the risk of complications or worsening health. In contrast, in cases where false alarms are not as detrimental, a perfect recall might not be as critical.

Consider the role of fire alarms in a building. If a fire alarm fails to go off when there is a fire (a false negative), it can endanger lives. Therefore, for fire safety, maintaining a high recall of fire alarms is vital to ensure that fires are detected promptly, even if it occasionally sounds an alarm for something non-threatening (a false positive). The priority is on minimizing the potentially catastrophic consequences of missing a fire.

In datasets where one class is much more prevalent than another, recall becomes a critical metric.

In situations where one class (such as non-spam emails) far outweighs another class (spam emails), relying solely on accuracy can be misleading. This is because a model might predict the dominant class all the time and still achieve a high accuracy score, while failing to correctly identify the minority class. Here, recall plays an essential role as it focuses only on the positive class, revealing how well the model identifies actual positive instances regardless of overall performance metrics like accuracy.

Imagine trying to catch a rare bird species in a large forest where most birds are common species. If you only count the total number of birds you saw, you might feel satisfied with your results, even if you missed the rare bird completely. Recall, however, would highlight how many of the rare species were actually seen, thereby giving a clearer picture of your success in identifying them, which is far more crucial in the context of conservation efforts.

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