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Dropout是一种广泛使用的正则化技术，通常需要为许多体系结构获得最先进的技术。这项工作表明，dropout引入了两种截然不同但相互纠缠的正则化效应:由于dropout修改了预期的训练目标而产生的显式效应(在之前的工作中也研究过)，以及可能令人惊讶的是，dropout训练更新中的随机性带来的另一种隐式效应。这种隐式正则化效应类似于小批量随机梯度下降中的随机度效应。我们通过控制实验把这两种效应分开。然后，我们推导出分析的简化，用模型的导数和损失来描述每个影响，对于深度神经网络。我们证明了这些简化的、解析的正则化器准确地捕获了辍学的重要方面，表明它们在实践中忠实地替代了dropout。
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The Implicit and Explicit Regularization Effects of Dropout
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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, nature's least favorable distribution is dropout noise, where nature independently deletes entries of the covariate vector with some fixed probability $\delta$. This result implies that dropout training indeed provides out-of-sample expected loss guarantees for distributions that arise from multiplicative perturbations of in-sample data. In addition to the decision-theoretic analysis, the paper makes two more contributions. First, there is a concrete recommendation on how to select the tuning parameter $\delta$ to guarantee that, as the sample size grows large, the in-sample loss after dropout training exceeds the true population loss with some pre-specified probability. Second, the paper 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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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, nature's least favorable distribution is dropout noise, where nature independently deletes entries of the covariate vector with some fixed probability $\delta$. This result implies that dropout training indeed provides out-of-sample expected loss guarantees for distributions that arise from multiplicative perturbations of in-sample data. In addition to the decision-theoretic analysis, the paper makes two more contributions. First, there is a concrete recommendation on how to select the tuning parameter $\delta$ to guarantee that, as the sample size grows large, the in-sample loss after dropout training exceeds the true population loss with some pre-specified probability. Second, the paper 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.
