Area Under the ROC Curve

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The area under the ROC curve (AUC) is a measure for ranking quality.

In recommender systems, we are often interested in how well method can rank a given set of items. The best possible value is 1, and any non-random ranking that makes sense would have an AUC > 0.5.

An intuitive explanation:

The AUC specifies the probability that, when we draw two examples at random, their predicted pairwise ranking is correct.
(adapted from [1], which we found via [2])

AUC does not give a higher weight to items higher up in the ranking. Some measures that put more weight on higher-ranking items are normalized discounted cumulative gain (NDCG) and mean average precision (MAP).

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