# Hierarchical Gaussian Processes with Wasserstein-2 Kernels

arXiv: https://arxiv.org/abs/2010.14877 · HTML: https://mlsanity.com/paper/2010.14877/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2020.

## Built on by (most cited first, 5 of 5)

- [Distributional Gaussian Process Layers for Outlier Detection in Image Segmentation](https://mlsanity.com/paper/2104.13756/) (2021)
- [Distributional Gaussian Processes Layers for Out-of-Distribution Detection](https://mlsanity.com/paper/2206.13346/) (2022)
- [Adaptive Residual Transformation for Enhanced Feature-Based OOD Detection in SAR Imagery](https://mlsanity.com/paper/2411.00274/) (2024)
- [Computationally-efficient initialisation of GPs: The generalised variogram method](https://mlsanity.com/paper/2210.05394/) (2022)
- [An Analysis of Posterior Collapse, Parameterization and Initialization in Variational Deep Gaussian Processes](https://mlsanity.com/paper/2606.25882/) (2026)

## Abstract (arXiv)

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.