The P-R curve

Why do we need two separate metrics--precision as well as recall? Let's dig a little deeper into their meanings. When we say that a classification system has a high precision, what does it exactly mean? It means that if the system predicts that a particular data point belongs to the positive class, then there is a very high probability that it indeed does so. You can revisit the definition of precision to convince yourself that this is indeed the case. Now, imagine that we have a classification system in place at a pathological laboratory, which, given the necessary medical details of a patient, classifies it as a positive (or a negative) occurrence of cancer. Now, obviously, we would want such a system to have a very high precision. It would be disastrous (mentally, physically, and financially) to tell a healthy patient that they have been diagnosed with cancer.

Now, we would like our cancer classifier to have a high recall. Having a low recall would mean that there are a lot...