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“Local” vs. “global” parameters – breaking the Gaussian complexity barrier. (English) Zbl 1459.62054
Summary: We show that if $$F$$ is a convex class of functions that is $$L$$-sub-Gaussian, the error rate of learning problems generated by independent noise is equivalent to a fixed point determined by “local” covering estimates of the class (i.e., the covering number at a specific level), rather than by the Gaussian average, which takes into account the structure of $$F$$ at an arbitrarily small scale. To that end, we establish new sharp upper and lower estimates on the error rate in such learning problems.

##### MSC:
 62G08 Nonparametric regression and quantile regression 62C20 Minimax procedures in statistical decision theory 60G15 Gaussian processes
##### Keywords:
error rates; Gaussian averages; covering numbers
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