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We propose a framework to analyze and quantify the bias in adaptive dataanalysis. It generalizes that proposed by Russo and Zou'15, applying tomeasurements whose moment generating function exists, measurements with afinite $p$-norm, and measurements in general Orlicz spaces. We introduce a newclass of dependence measures which retain key properties of mutual informationwhile more effectively quantifying the exploration bias for heavy taileddistributions. We provide examples of cases where our bounds are nearly tightin situations where the original framework of Russo and Zou'15 does not apply.

Dependence Measures Bounding the Exploration Bias for General Measurements