Minimax Learning Rates for Bipartite Ranking and Plug-in Rules

Overview & Synopsis

While it is now well-known in the standard binary classi cation setup, that, under suitable margin assumptions and complexity conditions on the regression function, fast or even super-fast rates can be achieved by plug-in classi ers, no result of this nature has been proved yet in the context of bipartite ranking, though akin to that of classi cation. It is the main purpose of the present paper to investigate this issue. Viewing bipartite ranking as a nested continuous collection of cost-sensitive classi cation problems, we exhibit a global low noise condition under which certain plug-in ranking rules can be shown to achieve fast (but not super-fast) rates, establishing thus minimax upper bounds for the excess of ranking risk.