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。
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.
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.