标题： Dropout：显式形式与容量控制 显示英文标题

标题： Dropout: Explicit Forms and Capacity Control

摘要： 我们研究了dropout在各种机器学习问题中提供的容量控制。 首先，我们研究了矩阵补全中的dropout，其中它引入了一个数据相关的正则化项，在期望下等于因子乘积的加权核范数。 在深度学习中，我们表明由于dropout产生的数据相关正则化项直接控制了深层神经网络潜在类的Rademacher复杂度。 这些发展使我们能够为dropout算法在矩阵补全以及训练深层神经网络中的泛化误差提供具体的边界。 我们在真实世界的数据集上评估了我们的理论结果，包括MovieLens、MNIST和Fashion-MNIST。 显示英文摘要

摘要： We investigate the capacity control provided by dropout in various machine learning problems. First, we study dropout for matrix completion, where it induces a data-dependent regularizer that, in expectation, equals the weighted trace-norm of the product of the factors. In deep learning, we show that the data-dependent regularizer due to dropout directly controls the Rademacher complexity of the underlying class of deep neural networks. These developments enable us to give concrete generalization error bounds for the dropout algorithm in both matrix completion as well as training deep neural networks. We evaluate our theoretical findings on real-world datasets, including MovieLens, MNIST, and Fashion-MNIST.