Precision and recall

In pattern recognition, information retrieval, object detection and classification (machine learning), precision and recall are performance metrics that apply to data retrieved from a collection, corpus or sample space.

Precision (also called positive predictive value) is the fraction of relevant instances among the retrieved instances. Written as a formula:

$${\displaystyle {\text{Precision}}={\frac {\text{Relevant retrieved instances}}{{\text{All }}{\textbf {retrieved}}{\text{ instances}}}}}$$

Recall (also known as sensitivity) is the fraction of relevant instances that were retrieved. Written as a formula:

$${\displaystyle {\text{Recall}}={\frac {\text{Relevant retrieved instances}}{{\text{All }}{\textbf {relevant}}{\text{ instances}}}}}$$

Both precision and recall are therefore based on relevance.

Consider a computer program for recognizing dogs (the relevant element) in a digital photograph. Upon processing a picture which contains ten cats and twelve dogs, the program identifies eight dogs. Of the eight elements identified as dogs, only five actually are dogs (true positives), while the other three are cats (false positives). Seven dogs were missed (false negatives), and seven cats were correctly excluded (true negatives). The program's precision is then 5/8 (true positives / selected elements) while its recall is 5/12 (true positives / relevant elements).

Adopting a hypothesis-testing approach, where in this case, the null hypothesis is that a given item is irrelevant (not a dog), absence of type I and type II errors (perfect specificity and sensitivity) corresponds respectively to perfect precision (no false positives) and perfect recall (no false negatives).