# Recall (machine learning)

> A metric for classification models that answers the following question:[^1]

A metric for [classification models](https://wiki.g15e.com/pages/Classification%20model.txt) that answers the following question:[^1]

> When [ground truth](https://wiki.g15e.com/pages/Ground%20truth%20(machine%20learning.txt)) was the [positive class](https://wiki.g15e.com/pages/Positive%20class%20(machine%20learning.txt)), what percentage of predictions did the model correctly identify as the positive class?

## Formula

Recall is the proportion of all actual positives that were classified correctly as positives:

$$
\frac{\text{correctly classified actual positives}}{\text{all actual positives}}
$$

which means:

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

where:

- [True positive](https://wiki.g15e.com/pages/True%20positive.txt) means the model *correctly* predicted the [positive class](https://wiki.g15e.com/pages/Positive%20class%20(machine%20learning.txt)).
- [False negative](https://wiki.g15e.com/pages/False%20negative.txt) means that the model *mistakenly* predicted the [negative class](https://wiki.g15e.com/pages/Negative%20class%20(machine%20learning.txt)).

[Precision](https://wiki.g15e.com/pages/Precision%20(machine%20learning.txt)) improves as [false positives](https://wiki.g15e.com/pages/False%20positive.txt) decrease, while [recall](https://wiki.g15e.com/pages/Recall%20(machine%20learning.txt)) improves when [false negatives](https://wiki.g15e.com/pages/False%20negative.txt) decrease. They often show an inverse relationship, where improving one of them worsens the other. (See also [F1 score](https://wiki.g15e.com/pages/F1%20score.txt))

## When (not) to use

Use when [false negative](https://wiki.g15e.com/pages/False%20negative.txt) are more expensive than [false positives](https://wiki.g15e.com/pages/False%20positive.txt).[^2]

Recall is particularly useful for determining the predictive power of classification models in which the positive class is rare. Recall is a much more useful metric for [class-imbalanced datasets](https://wiki.g15e.com/pages/Class-imbalanced%20dataset.txt) than [accuracy](https://wiki.g15e.com/pages/Accuracy%20(machine%20learning.txt)).[^1] But the number of actual positives is very, very low, say 1-2 examples in total, recall is less meaningful and less useful as a metric.[^2]

## See also

- [False positive rate](https://wiki.g15e.com/pages/False%20positive%20rate.txt) (a.k.a. **probability of false alarm**, where the recall is known as called **probability of detection**)
- [Accuracy](https://wiki.g15e.com/pages/Accuracy%20(machine%20learning.txt))
- [Precision](https://wiki.g15e.com/pages/Precision%20(machine%20learning.txt))
- [ROC curve](https://wiki.g15e.com/pages/ROC%20curve.txt): Recall (a.k.a. True positive rate) is the y-axis in an ROC curve.

## Footnotes

[^1]: https://developers.google.com/machine-learning/glossary#recall
[^2]: [ML crash course - Classification](https://wiki.g15e.com/pages/ML%20crash%20course%20-%20Classification.txt)