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While it is now well-known in the standard binary classication setup, that, under suitable margin assumptions and complexity conditions on the regression function, fast or even super-fast rates (i.e. rates faster than n^(-1/2) or even faster than n^-1) can be achieved by plug-in classiers, no result of this nature has been proved yet in the context of bipartite ranking, though akin to that of classication. It is the main purpose of the present paper to investigate this issue. Viewing bipartite ranking as a nested continuous collection of cost-sensitive classication 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.
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