Weighted ERM with margin or inverse-variance weights tightens conditional risk bounds on high-confidence subregions by a constant factor, and yields an O(1/n) rate for estimating heteroscedastic variance.
H-consistency bounds for surrogate loss minimizers
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Reweighting Improves Conditional Risk Bounds
Weighted ERM with margin or inverse-variance weights tightens conditional risk bounds on high-confidence subregions by a constant factor, and yields an O(1/n) rate for estimating heteroscedastic variance.