The true positive (TP), together with true negative (TN) (*) is a type of accurately predicted outcome, meaning that the prediction matches the true observation/ condition in terms of the class (positive/ negative).  
 
TP occurs when a positive class prediction (classification) was accurately made.  


True Positive (TP)

Sensitivity is the probability of a correct prediction of positive classification; in other words, the probability of the true positive (TP).  

University of Michigan - Ann Arbor

Recall, also known as the True Positive Rate (TPR), is defined as True Positives / (True Positives + False Negatives), i.e., what % of actual outcomes (labels) are correctly recognized.

Recall is important in tasks that required as many possible positives to be identified.

Recall is especially important in medicinal and legal applications (ex: fraud detection and tumor detection), and it is occasionally paired with someone who manually filters out all of the False Positives. Recall is also related to F1 Score and ROC Curves.


Recall of a Classification Model

Pearl, J., & Mackenzie, D. (2018). $$\mathit{The \ Book \ of \ Why: \ The \ New \ Science \ of \ Cause \ and \ Effect.}$$ Basic Books.

The Book of Why

Sensitivity

In binary classification, the F1 score summarizes how well a model balances precision and recall. It is the harmonic mean of those two values, so it reaches its best value of 1.0 only when both precision and recall are perfect. If either precision or recall is 0, the F1 score is 0. The metric is often used in tasks such as search ranking, document labeling, query classification, named entity recognition, and word segmentation. A common critique is that it weights precision and recall equally. Another limitation is that it ignores true negatives, which can make it less suitable when class imbalance is severe.

$$F_1 = 2\frac{1}{\left(\frac{1}{precision}+\frac{1}{recall}\right)}$$

F1 Score

There are four combinations of precision and recall:
(1) High Precision and High Recall
(2) High Precision and Low Recall
(3) Low Precision and High Recall
(4) Low Precision and Low Recall

Relation between Precision and Recall

F-Measure is a metric that incorporates aspects of both precision and recall, defined as:
$$F_\beta = \frac{(\beta^2 + 1)PR}{\beta^2P + R}$$
The $\beta$ parameter differentially weights the importance of recall $R$ and precision $P$, based perhaps on the needs of an application. Values of $\beta > 1$ favor recall, while values of $\beta < 1$ favor precision. When $\beta = 1$, the measure is simply the F-1 score, where precision and recall are equally balanced.

Learn Before

Related

Learn After