Data augmentation is a powerful technique to improve performance in applications such as image and text classification tasks. Yet, there is little rigorous understanding of why and how various augmentations work. In this work, we consider a family of linear transformations and study their effects on the ridge estimator in an over-parametrized linear regression setting. First, we show that transformations which preserve the labels of the data can improve estimation by enlarging the span of the training data. Second, we show that transformations which mix data can improve estimation by playing a regularization effect. Finally, we validate our theoretical insights on MNIST. Based on the insights, we propose an augmentation scheme that searches over the space of transformations by how uncertain the model is about the transformed data. We validate our proposed scheme on image and text datasets. For example, our method outperforms RandAugment by 1.24% on CIFAR-100 using Wide-ResNet-28-10. Furthermore, we achieve comparable accuracy to the SoTA Adversarial AutoAugment on CIFAR datasets.

本文考察了一系列线性变换及其对于过参数化线性回归问题中的岭回归估计量的影响，证实了保留数据标签的变换能够通过扩大训练数据空间来提高估计精度，而混合数据的变换则能够达到一种正则化效果。在此基础上，提出一种根据模型不确定性搜索变换空间的数据增强方案，并在图像和文本数据集上测试，证实了其表现优于已有的RandAugment方法及能够达到现有SoTA方法的精度。

关于数据增强中线性变换的泛化效果