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

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arxiv 1504.02191 v1 pith:USOC4LQJ submitted 2015-04-09 stat.ML math.STstat.TH

Shahar Mendelson This is my paper · ORCID
classification stat.MLmath.STstat.TH
keywords classerrorestimatesgaussianlocalproblemsrateaverages
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abstract

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.

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Cited by 1 Pith paper

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  1. On Least Squares Estimation under Heteroscedastic and Heavy-Tailed Errors

    math.ST 2019-09 conditional novelty 7.0 of 10

    Under finite moments and a local envelope growth condition, the least squares estimator in nonparametric regression can achieve minimax rates with heavy-tailed, covariate-dependent errors.

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