  Deep generative models are rapidly gaining traction in medical imaging.
Nonetheless, most generative architectures struggle to capture the underlying
probability distributions of volumetric data, exhibit convergence problems, and
offer no robust indices of model uncertainty. By comparison, the autoregressive
generative model PixelCNN can be extended to volumetric data with relative
ease, it readily attempts to learn the true underlying probability distribution
and it still admits a Bayesian reformulation that provides a principled
framework for reasoning about model uncertainty. Our contributions in this
paper are two fold: first, we extend PixelCNN to work with volumetric brain
magnetic resonance imaging data. Second, we show that reformulating this model
to approximate a deep Gaussian process yields a measure of uncertainty that
improves the performance of semi-supervised learning, in particular
classification performance in settings where the proportion of labelled data is
low. We quantify this improvement across classification, regression, and
semantic segmentation tasks, training and testing on clinical magnetic
resonance brain imaging data comprising T1-weighted and diffusion-weighted
sequences.
