In this note, I study how the precision of a binary classifier depends on the ratio γ of positive to negative cases in the test set, as well as the classifier’s true and false-positive rates. This relationship allows prediction of how the precision-recall curve will change with γ , which seems not to be well known. It also allows prediction of how F_β and the precision gain and recall gain measures of Flach and Kull (2015) vary with γ.
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