Machine Learning's Dropout Training is Distributionally Robust Optimal
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This paper shows that dropout training in Generalized Linear Models is the minimax solution of a two-player, zero-sum game where an adversarial nature corrupts a statistician's covariates using a multiplicative nonparametric errors-in-variables model. In this game—known as a Distributionally Robust Optimization problem—nature's least favorable distribution is dropout noise, where nature independently deletes entries of the covariate vector with some fixed probability δ. Our decision-theoretic analysis shows that dropout training—the statistician's minimax strategy in the game—indeed provides out-of-sample expected loss guarantees for distributions that arise from multiplicative perturbations of in-sample data. This paper also provides a novel, parallelizable, Unbiased Multi-Level Monte Carlo algorithm to speed-up the implementation of dropout training. Our algorithm has a much smaller computational cost compared to the naive implementation of dropout, provided the number of data points is much smaller than the dimension of the covariate vector.
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