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I know that the random classifier score in ROC AUC (Area under the curve) is always 0.5. My question is: how to calculate the Area under the precision-recall curve for the random classifier?

Jack Twain
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    The PR curve is fragile, and not well-defined (at 0 recall, the precision is not defined). Maybe something like classic Average Precision is the better choice? – Has QUIT--Anony-Mousse Oct 28 '14 at 21:40
  • @Anony-Mousse how is precision not defined at 0 recall? if recall=0 then True Positive is zero. if you check the Precision formula, you have a False Positive in the denominator, so it can't be undefined. – Jack Twain Oct 29 '14 at 08:11
  • If the first element is positive, what is the accuracy at recall=0? As long as it is a miss, you are okay, but if it is correct, then your curve doesn't start at recall=0. If you retrieve 0 elements, then the denominator is 0, and cannot simply be resolved by L'Hôpitals rule - it could be anything from 0 to 1. – Has QUIT--Anony-Mousse Oct 29 '14 at 11:56

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