# On the Generalization Effects of Linear Transformations in Data Augmentation

arXiv: https://arxiv.org/abs/2005.00695 · HTML: https://mlsanity.com/paper/2005.00695/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 May 2020.

## Built on by (most cited first, 30 of 47)

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- [Causality-inspired Single-source Domain Generalization for Medical Image Segmentation](https://mlsanity.com/paper/2111.12525/) (2021)
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- [Data Augmentation Approaches in Natural Language Processing: A Survey](https://mlsanity.com/paper/2110.01852/) (2021)
- [Graph Data Augmentation for Graph Machine Learning: A Survey](https://mlsanity.com/paper/2202.08871/) (2022)
- [Accelerating Dataset Distillation via Model Augmentation](https://mlsanity.com/paper/2212.06152/) (2022)
- [Robust Fine-Tuning of Deep Neural Networks with Hessian-based Generalization Guarantees](https://mlsanity.com/paper/2206.02659/) (2022)
- [Robust (Controlled) Table-to-Text Generation with Structure-Aware Equivariance Learning](https://mlsanity.com/paper/2205.03972/) (2022)
- [ReMix: A General and Efficient Framework for Multiple Instance Learning based Whole Slide Image Classification](https://mlsanity.com/paper/2207.01805/) (2022)
- [Direct Differentiable Augmentation Search](https://mlsanity.com/paper/2104.04282/) (2021)
- [Sample Efficiency of Data Augmentation Consistency Regularization](https://mlsanity.com/paper/2202.12230/) (2022)
- [Noisy Feature Mixup](https://mlsanity.com/paper/2110.02180/) (2021)
- [Toward Understanding Generative Data Augmentation](https://mlsanity.com/paper/2305.17476/) (2023)
- [The good, the bad and the ugly sides of data augmentation: An implicit spectral regularization perspective](https://mlsanity.com/paper/2210.05021/) (2022)
- [Enhancing MR Image Segmentation with Realistic Adversarial Data Augmentation](https://mlsanity.com/paper/2108.03429/) (2021)
- [Scalable Multitask Learning Using Gradient-based Estimation of Task Affinity](https://mlsanity.com/paper/2409.06091/) (2024)
- [The Benefits of Mixup for Feature Learning](https://mlsanity.com/paper/2303.08433/) (2023)
- [Data Augmentation as Feature Manipulation](https://mlsanity.com/paper/2203.01572/) (2022)
- [DivAug: Plug-in Automated Data Augmentation with Explicit Diversity Maximization](https://mlsanity.com/paper/2103.14545/) (2021)
- [Boosting Multitask Learning on Graphs through Higher-Order Task Affinities](https://mlsanity.com/paper/2306.14009/) (2023)
- [Provably Learning Diverse Features in Multi-View Data with Midpoint Mixup](https://mlsanity.com/paper/2210.13512/) (2022)
- [How Tempering Fixes Data Augmentation in Bayesian Neural Networks](https://mlsanity.com/paper/2205.13900/) (2022)
- [The Curious Case of Benign Memorization](https://mlsanity.com/paper/2210.14019/) (2022)
- [Promoting Generalization for Exact Solvers via Adversarial Instance Augmentation](https://mlsanity.com/paper/2310.14161/) (2023)
- [Graph Out-of-Distribution Generalization with Controllable Data Augmentation](https://mlsanity.com/paper/2308.08344/) (2023)
- [Adaptive Weighting Scheme for Automatic Time-Series Data Augmentation](https://mlsanity.com/paper/2102.08310/) (2021)
- [Sill-Net: Feature Augmentation with Separated Illumination Representation](https://mlsanity.com/paper/2102.03539/) (2021)
- [RegMix: Data Mixing Augmentation for Regression](https://mlsanity.com/paper/2106.03374/) (2021)
- [Contrastive-mixup learning for improved speaker verification](https://mlsanity.com/paper/2202.10672/) (2022)
- [An Empirical Study and Analysis on Open-Set Semi-Supervised Learning](https://mlsanity.com/paper/2101.08237/) (2021)

## Abstract (arXiv)

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 that preserve the labels of the data can improve estimation by enlarging the span of the training data. Second, we show that transformations that 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 random sampling methods by 1.24% on CIFAR-100 using Wide-ResNet-28-10. Furthermore, we achieve comparable accuracy to the SoTA Adversarial AutoAugment on CIFAR-10, CIFAR-100, SVHN, and ImageNet datasets.