  Stacking Gaussian Processes severely diminishes the model's ability to detect
outliers, which when combined with non-zero mean functions, further
extrapolates low non-parametric variance to low training data density regions.
We propose a hybrid kernel inspired from Varifold theory, operating in both
Euclidean and Wasserstein space. We posit that directly taking into account the
variance in the computation of Wasserstein-2 distances is of key importance
towards maintaining outlier status throughout the hierarchy. We show improved
performance on medium and large scale datasets and enhanced out-of-distribution
detection on both toy and real data.
