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While standard statistical inference techniques and machine learninggeneralization bounds assume that tests are run on data selected independentlyof the hypotheses, practical data analysis and machine learning are usuallyiterative and adaptive processes where the same holdout data is often used fortesting a sequence of hypotheses (or models), which may each depend on theoutcome of the previous tests on the same data. In this work, we presentRadaBound a rigorous, efficient and practical procedure for controlling thegeneralization error when using a holdout sample for multiple adaptive testing.Our solution is based on a new application of the Rademacher Complexitygeneralization bounds, adapted to dependent tests. We demonstrate thestatistical power and practicality of our method through extensive simulationsand comparisons to alternative approaches.

A Rademacher Complexity Based Method fo rControlling Power and Confidence Level in Adaptive Statistical Analysis