Scaffolding Sets

11/04/2021

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by   Maya Burhanpurkar, et al.

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9

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Predictors map individual instances in a population to the interval [0,1]. For a collection 𝒞 of subsets of a population, a predictor is multi-calibrated with respect to 𝒞 if it is simultaneously calibrated on each set in 𝒞. We initiate the study of the construction of scaffolding sets, a small collection 𝒮 of sets with the property that multi-calibration with respect to 𝒮 ensures correctness, and not just calibration, of the predictor. Our approach is inspired by the folk wisdom that the intermediate layers of a neural net learn a highly structured and useful data representation.