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AUC stands for the Area Under the Curve and usually refers to the area under the receiver operating characteristic (ROC) curve.
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Why are the trivial points included when calculating AUC?
I'm aware of some of the issues associated with using AUC for model comparison (see for example the articles referenced on Wikipedia: here, here, or here). … Of course comparing models based on on a single criterion such as AUC is probably a bad idea in general. …