PAC Bayesian Performance Guarantees for Deep (Stochastic) Networks in Medical Imaging

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.