For every LUM loss, the excess misclassification error is controlled by a multiple of the excess surrogate loss, with a square-root rate at p=0 that improves under Tsybakov noise.
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Comparison theorems on large-margin learning
For every LUM loss, the excess misclassification error is controlled by a multiple of the excess surrogate loss, with a square-root rate at p=0 that improves under Tsybakov noise.