We address the following seemingly simple question: what is the Bayes-optimal scorer for a bipartite ranking risk? The answer to this question helps elucidate the relationship between bipartite ranking and other established learning problems. We show that the answer is non-trivial in general, but may be easily determined for certain special cases using the theory of proper losses. Our analysis immediately establishes equivalence relationships between several seemingly disparate approaches to bipartite ranking, such as minimising a suitable class-probability estimation risk, and minimising thep-norm push risk proposed in Rudin (2009).
['Aditya Krishna Menon', 'Robert C. Williamson']
Bayes-Optimal Scorers for Bipartite Ranking