Data science & AI · Reference
What are precision and recall?
Precision and recall are two metrics for evaluating a classifier: precision measures how many of the items predicted positive are actually positive, while recall measures how many of the actual positives the model successfully finds.
What each metric measures
Both metrics are computed from the cells of a confusion matrix. Precision asks: of all the cases the model labelled positive, how many really were? It is true positives divided by all predicted positives, and it falls when there are many false positives. Recall (also called sensitivity) asks: of all the truly positive cases, how many did the model catch? It is true positives divided by all actual positives, and it falls when there are many false negatives. The two answer different questions about the same classifier.
The precision–recall trade-off
Precision and recall usually pull against each other. A classifier can raise recall by labelling more cases positive — but this tends to admit more false positives, lowering precision. Conversely, being more conservative raises precision at the cost of missing cases, lowering recall.
Where to sit on this trade-off depends on the cost of each error: a disease screen may favour recall to avoid missing cases, while a spam filter may favour precision to avoid blocking legitimate mail. The F1 score summarises the balance in a single number.
Why accuracy is not enough
On imbalanced data — where one class is rare — accuracy can be misleadingly high. A test that always predicts "negative" for a condition present in 1% of cases is 99% accurate yet useless, because it never finds a true case: its recall is zero. Precision and recall expose exactly this failure. For this reason they are the standard metrics in information retrieval, medical testing, and fraud detection, where the positive class is rare and the cost of missing it is high.
Precision and recall in research
When reporting classifier performance in research, precision and recall (often with the F1 score) are preferred to accuracy alone, especially for imbalanced problems. Because they trade off against each other, both should be reported together, along with the decision threshold used; quoting one without the other can paint an incomplete or flattering picture. Metrics should be computed on held-out data so they reflect generalisation rather than training-set performance.
Key facts
At a glance
- Precision: true positives ÷ all predicted positives
- Recall: true positives ÷ all actual positives
- Recall is also called sensitivity
- Trade-off: raising one tends to lower the other
- Important on imbalanced data, where accuracy misleads
- Both derived from the confusion matrix
Common questions
FAQ
What is the difference between precision and recall?+
Precision measures how many of the items predicted positive are truly positive, capturing the cost of false alarms. Recall measures how many of the actual positives are found, capturing the cost of missed cases. They answer different questions about the same classifier.
Why is there a trade-off between precision and recall?+
Labelling more cases positive tends to catch more true positives (higher recall) but also more false positives (lower precision). Being more conservative does the reverse. Adjusting the decision threshold moves a classifier along this trade-off.
When are precision and recall more useful than accuracy?+
On imbalanced data, where one class is rare. A model can score high accuracy by always predicting the common class while completely failing to detect the rare one. Precision and recall reveal that failure where accuracy hides it.
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