Precision and Recall - Probabilistic Interpretation

Probabilistic Interpretation

It is possible to interpret precision and recall not as ratios but as probabilities:

• Precision is the probability that a (randomly selected) retrieved document is relevant.

• Recall is the probability that a (randomly selected) relevant document is retrieved in a search.

Note that the random selection refers to a uniform distribution over the appropriate pool of documents; i.e. by randomly selected retrieved document, we mean selecting a document from the set of retrieved documents in a random fashion. The random selection should be such that all documents in the set are equally likely to be selected.

Note that, in a typical classification system, the probability that a retrieved document is relevant depends on the document. The above interpretation extends to that scenario also (needs explanation).

Another interpretation for precision and recall is as follows. Precision is the average probability of relevant retrieval. Recall is the average probability of complete retrieval. Here we average over multiple retrieval queries.