  Application of deep neural networks to medical imaging tasks has in some
sense become commonplace. Still, a "thorn in the side" of the deep learning
movement is the argument that deep networks are somehow prone to overfitting
and are thus unable to generalize well when datasets are small. The claim is
not baseless and likely stems from the observation that PAC bounds on
generalization error are usually so large for deep networks that they are
vacuous (i.e., logically meaningless). Contrary to this, recent advances using
the PAC-Bayesian framework have instead shown non-vacuous bounds on
generalization error for large (stochastic) networks and standard datasets
(e.g., MNIST and CIFAR-10). We apply these techniques to a much smaller medical
imagining dataset (the ISIC 2018 challenge set). Further, we consider
generalization of deep networks on segmentation tasks which has not commonly
been done using the PAC-Bayesian framework. Importantly, we observe that the
resultant bounds are also non-vacuous despite the sharp reduction in sample
size. In total, our results demonstrate the applicability of PAC-Bayesian
bounds for deep stochastic networks in the medical imaging domain.
