  There is a set of data augmentation techniques that ablate parts of the input
at random. These include input dropout, cutout, and random erasing. We term
these techniques ablated data augmentation. Though these techniques seems
similar in spirit and have shown success in improving model performance in a
variety of domains, we do not yet have a mathematical understanding of the
differences between these techniques like we do for other regularization
techniques like L1 or L2. First, we study a formal model of mean ablated data
augmentation and inverted dropout for linear regression. We prove that ablated
data augmentation is equivalent to optimizing the ordinary least squares
objective along with a penalty that we call the Contribution Covariance Penalty
and inverted dropout, a more common implementation than dropout in popular
frameworks, is equivalent to optimizing the ordinary least squares objective
along with Modified L2. For deep networks, we demonstrate an empirical version
of the result if we replace contributions with attributions and coefficients
with average gradients, i.e., the Contribution Covariance Penalty and Modified
L2 Penalty drop with the increase of the corresponding ablated data
augmentation across a variety of networks.
