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When handling probabilities close to 1, it is often more helpful to use the complement (i.e. 1-P). For instance, we say "there is a 1 in 1,000,000 chance of an event occurring", instead of "999,999 in 1,000,000 chance of nothing happening" or even 99.9999% chance. Doing so also allows one to make comparisons on a log-scale.

My question is whether one can and/or should do the same for very high AUROC and AP (average precision) values. So instead of taking the area under the curve, taking the complement, which is the area ABOVE the curve.

Cyruno
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    ROC AUC has a direct interpretation as a probability https://stats.stackexchange.com/questions/180638/how-to-derive-the-probabilistic-interpretation-of-the-auc so you can easily construct an interpretation of the complementary event using the method outlined in your first paragraph. (As an aside, one can compute the log of a number near 1, but the function $\log(x)$ is more attenuated for $x$ close to 0 than it is for $x$ close to 1. By contrast, logits are attenuated at both extremes.) – Sycorax Feb 22 '23 at 16:53

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