Robust reductions from ranking to classification

@article{Balcan2007RobustRF,
  title={Robust reductions from ranking to classification},
  author={Maria-Florina Balcan and Nikhil Bansal and Alina Beygelzimer and Don Coppersmith and John Langford and Gregory B. Sorkin},
  journal={Machine Learning},
  year={2007},
  volume={72},
  pages={139-153}
}
We reduce ranking, as measured by the Area Under the Receiver Operating Characteristic Curve (AUC), to binary classification. The core theorem shows that a binary classification regret of r on the induced binary problem implies an AUC regret of at most 2r. This is a large improvement over approaches such as ordering according to regressed scores, which have a regret transform of r ↦ nr where n is the number of elements. 
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