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Abstract

We information-theoretically reformulate two measures of capacity from statistical learning theory: empirical VC-entropy and empirical Rademacher complexity. We show these capacity measures count the number of hypotheses about a dataset that a learning algorithm falsies when it nds the classier in its repertoire minimizing empirical risk. It then follows from that the future performance of predictors on unseen data is controlled in part by how many hypotheses the learner falsies. As a corollary we show that empirical VC-entropy quanties the message length of the true hypothesis in the optimal code of a particular probability distribution, the so-called actual repertoire.