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 never 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.
@article{arxiv.2104.13756,
title = {Distributional Gaussian Process Layers for Outlier Detection in Image Segmentation},
author = {Sebastian G. Popescu and David J. Sharp and James H. Cole and Konstantinos Kamnitsas and Ben Glocker},
journal= {arXiv preprint arXiv:2104.13756},
year = {2021}
}