Precision, recall, and F1-score are all measures used to evaluate the performance of a classification model. They are based on the confusion matrix which is a table that shows the number of true positives (TP), false positives (FP), false negatives (FN), and true negatives (TN).
Precision is the fraction of true positives among the items that the model classified as positive. It measures the how precise the classification model was in predicting positive cases. It is defined as
$$Precision = \frac{TP}{TP + FP}$$
A high precision means that there were few false positives relative to true positives, therefore the model is accurate when it identifies a positive instance. Precision is useful when you want to minimize false positives, i.e., when you want to make sure that when the model identifies a positive instance, it is indeed a true positive. A typical use case would be in medical diagnosis where a false positive could lead to an unnecessary treatment or intervention.
Recall (also known as sensitivity) is the fraction of true positives among all actual positive items. It measures the ability of the model to identify all positive cases, i.e., it measures how well the model identifies positive instances, whether they particularly were correctly classified or not. It is defined as
$$Recall = \frac{TP}{TP + FN}$$
A high recall means that there were few false negatives relative to true positives, therefore the model is able to correctly identify most of the positive instances. Recall is useful when you want to minimize false negatives, i.e., when you want to make sure that when the model misses a positive case, it is indeed absent. A typical use case would be in cancer diagnosis where a false negative could lead to delayed or no treatment.
F1-score is a summary measure of precision and recall that considers their harmonic mean, it is used for finding a balance between precision and recall. It is defined as the harmonic mean of precision and recall. It is given by
$$F1\_Score = \frac{2*Precision*Recall}{Precision + Recall}$$
A high F1-score means both precision and recall are high, which is ideal for a classification model. F1-score is useful when you want to find a balance between precision and recall, that is when you don’t want to optimize for either but get an overall sense of how well the model performs. A typical use case would be in certain web applications where the owner of the product can decide between False Positive and False Negative and optimize the model accordingly.
In summary, precision is used when we want to minimize false positives, recall when we want to minimize false negatives, and F1-score when we want to have a balance between precision and recall. Choosing the best metric depends on the specific task at hand and the desired outcomes.