Machine learning models deployed on medical imaging tasks must be equipped
with out-of-distribution detection capabilities in order to avoid erroneous
predictions. It is unsure whether out-of-distribution detection models reliant
on deep neural networks are suitable for detecting domain shifts in medical
imaging. Gaussian Processes can reliably separate in-distribution data points
from out-of-distribution data points via their mathematical construction.
Hence, we propose a parameter efficient Bayesian layer for hierarchical
convolutional Gaussian Processes that incorporates Gaussian Processes operating
in Wasserstein-2 space to reliably propagate uncertainty. This directly
replaces convolving Gaussian Processes with a distance-preserving affine
operator on distributions. Our experiments on brain tissue-segmentation show
that the resulting architecture approaches the performance of well-established
deterministic segmentation algorithms (U-Net), which has not been achieved with
previous hierarchical Gaussian Processes. Moreover, by applying the same
segmentation model to out-of-distribution data (i.e., images with pathology
such as brain tumors), we show that our uncertainty estimates result in
out-of-distribution detection that outperforms the capabilities of previous
Bayesian networks and reconstruction-based approaches that learn normative
distributions. To facilitate future work our code is publicly available.