AUC stands for the Area Under the Curve. Technically, it can be used for the area under any number of curves that are used to measure the performance of a model, for example, it could be used for the area under a precision-recall curve. However, when not otherwise specified, AUC is almost always taken to mean the area under the Receiver Operating Characteristic (ROC) curve. The acronym AUROC is sometimes used to indicate this AUC with greater precision. The curves for which the AUC might be calculated are usually plotted within a unit square.
The AUROC has several equivalent interpretations:
The expectation that a uniformly drawn random positive is ranked before a uniformly drawn random negative.
The expected proportion of positives ranked before a uniformly drawn random negative.
The expected true positive rate if the ranking is split just before a uniformly drawn random negative.
The expected proportion of negatives ranked after a uniformly drawn random positive.
The expected false positive rate if the ranking is split just after a uniformly drawn random positive.
When we make a binary prediction, there can be 4 types of outcomes:
We predict 0 while we should have the class is actually 0: this is called a True Negative, i.e. we correctly predict that the class is negative (0). For example, an antivirus did not detect a harmless file as a virus.
We predict 0 while we should have the class is actually 1: this is called a False Negative, i.e. we incorrectly predict that the class is negative (0). For example, an antivirus failed to detect a virus.
We predict 1 while we should have the class is actually 0: this is called a False Positive, i.e. we incorrectly predict that the class is positive (1). For example, an antivirus considered a harmless file to be a virus.
We predict 1 while we should have the class is actually 1: this is called a True Positive, i.e. we correctly predict that the class is positive (1). For example, an antivirus rightfully detected a virus
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Recommended reading list:
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