  Generative data augmentation, which scales datasets by obtaining fake labeled
examples from a trained conditional generative model, boosts classification
performance in various learning tasks including (semi-)supervised learning,
few-shot learning, and adversarially robust learning. However, little work has
theoretically investigated the effect of generative data augmentation. To fill
this gap, we establish a general stability bound in this not independently and
identically distributed (non-i.i.d.) setting, where the learned distribution is
dependent on the original train set and generally not the same as the true
distribution. Our theoretical result includes the divergence between the
learned distribution and the true distribution. It shows that generative data
augmentation can enjoy a faster learning rate when the order of divergence term
is $o(\max\left( \log(m)\beta_m, 1 / \sqrt{m})\right)$, where $m$ is the train
set size and $\beta_m$ is the corresponding stability constant. We further
specify the learning setup to the Gaussian mixture model and generative
adversarial nets. We prove that in both cases, though generative data
augmentation does not enjoy a faster learning rate, it can improve the learning
guarantees at a constant level when the train set is small, which is
significant when the awful overfitting occurs. Simulation results on the
Gaussian mixture model and empirical results on generative adversarial nets
support our theoretical conclusions. Our code is available at
https://github.com/ML-GSAI/Understanding-GDA.

Machine Learning;Machine Learning