What I know? Firstly,

Precision= $\frac{TP}{TP+FP}$


What book says?

A model that declares every record has high recall but low precision.

I understand that if predicted positive is high, precision will be low. But how will recall be high if predicted positive is high.

A model that assigns a positive class to every test record that matches one of the positive records in the training set has very high precision but low recall.

I am not able to properly comprehend how there is inverse relation between precision and recall.

Here is a doc that I found but I could not also understand from this doc as well.



1 Answer 1


There is an overall inverse relationship, but not a strictly monotone one. See e.g. the precision-recall curves in the sklearn examples.

A model that declares every record [to be positive class] has high recall but low precision.

If the model declares every record positive, then $TP=P$ and $FP=N$ (and $FN=TN=0$). So recall is 1; and the precision is $P/(P+N)$, i.e. the proportion of positives in the sample. (That may be "low" or not.)

Rather than addressing your second quote immediately, I think it might be beneficial to just examine (nearly) the opposite case to the above. Suppose your classifier only makes one positive prediction; assuming the model rank-orders reasonably well, it's very likely this is a true positive. Then $TP=1$, $FP=0$, $TN$ and $FN$ are both large. Then precision is 1, and recall is very small.

The second quote makes the assumption there more solid: every positive prediction is a true positive (assuming no opposite-class clones), but there are very few positive predictions.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.