Does Data Augmentation Lead to Positive Margin?
This provides theoretical insights into data augmentation for machine learning practitioners, but it is incremental as it builds on existing understanding.
The paper tackles the problem of understanding how data augmentation improves model robustness by analyzing the margin it enforces on empirical risk minimizers, showing that common techniques may require exponentially many augmented points to achieve significant margin.
Data augmentation (DA) is commonly used during model training, as it significantly improves test error and model robustness. DA artificially expands the training set by applying random noise, rotations, crops, or even adversarial perturbations to the input data. Although DA is widely used, its capacity to provably improve robustness is not fully understood. In this work, we analyze the robustness that DA begets by quantifying the margin that DA enforces on empirical risk minimizers. We first focus on linear separators, and then a class of nonlinear models whose labeling is constant within small convex hulls of data points. We present lower bounds on the number of augmented data points required for non-zero margin, and show that commonly used DA techniques may only introduce significant margin after adding exponentially many points to the data set.