`local' vs. `global' parameters -- breaking the gaussian complexity barrier

04/09/2015

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by   Shahar Mendelson, et al.

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We show that if F is a convex class of functions that is L-subgaussian, the error rate of learning problems generated by independent noise is equivalent to a fixed point determined by `local' covering estimates of the class, rather than by the gaussian averages. To that end, we establish new sharp upper and lower estimates on the error rate for such problems.