The classical binary classi cation problem is investigated when it is known in advance that the posterior probability function (or regression function) belongs to some class of functions. We i n troduce and analyze a method which e ectively exploits this knowledge. The method is based on minimizing the empirical risk over a carefully selected \skeleton" of the class of regression functions. The skeleton is a covering of the class based on a data-dependent metric, especially tted for classi cation. A new scale-sensitive dimension is introduced which is more useful for the studied classi cation problem than other, previously de ned, dimension measures. This fact is demonstrated by performance bounds for the skeleton estimate in terms of the new dimension. 1

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No abstract