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We investigate the problem of classification in the presence of unknownclass-conditional label noise in which the labels observed by the learner havebeen corrupted with some unknown class dependent probability. In order toobtain finite sample rates, previous approaches to classification with unknownclass-conditional label noise have required that the regression function isclose to its extrema on sets of large measure. We shall consider this problemin the setting of non-compact metric spaces, where the regression function neednot attain its extrema.  In this setting we determine the minimax optimal learning rates (up tologarithmic factors). The rate displays interesting threshold behaviour: Whenthe regression function approaches its extrema at a sufficient rate, theoptimal learning rates are of the same order as those obtained in thelabel-noise free setting. If the regression function approaches its extremamore gradually then classification performance necessarily degrades. Inaddition, we present an adaptive algorithm which attains these rates withoutprior knowledge of either the distributional parameters or the local density.This identifies for the first time a scenario in which finite sample rates areachievable in the label noise setting, but they differ from the optimal rateswithout label noise.

Classification with unknown class-conditional label noise on non-compact feature spaces