# Distributional Gaussian Process Layers for Outlier Detection in Image Segmentation

arXiv: https://arxiv.org/abs/2104.13756 · HTML: https://mlsanity.com/paper/2104.13756/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 15 references that are in the map.
- First posted on arXiv 28 Apr 2021.

## Builds on (most cited first, 12 of 12)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [A review of deep learning in medical imaging: Imaging traits, technology trends, case studies with progress highlights, and future promises](https://mlsanity.com/paper/2008.09104/) (2020)
- [Exploring Uncertainty Measures in Deep Networks for Multiple Sclerosis Lesion Detection and Segmentation](https://mlsanity.com/paper/1808.01200/) (2018)
- [Stochastic Segmentation Networks: Modelling Spatially Correlated Aleatoric Uncertainty](https://mlsanity.com/paper/2006.06015/) (2020)
- [Uncertainty Estimation Using a Single Deep Deterministic Neural Network](https://mlsanity.com/paper/2003.02037/) (2020)
- [Revisiting One-vs-All Classifiers for Predictive Uncertainty and Out-of-Distribution Detection in Neural Networks](https://mlsanity.com/paper/2007.05134/) (2020)
- [Deep convolutional Gaussian processes](https://mlsanity.com/paper/1810.03052/) (2018)
- [One Versus all for deep Neural Network Incertitude (OVNNI) quantification](https://mlsanity.com/paper/2006.00954/) (2020)
- [Knowing what you know in brain segmentation using Bayesian deep neural networks](https://mlsanity.com/paper/1812.01719/) (2018)
- [Hierarchical Gaussian Processes with Wasserstein-2 Kernels](https://mlsanity.com/paper/2010.14877/) (2020)

## Built on by (most cited first, 4 of 4)

- [Anomaly Detection in Medical Imaging -- A Mini Review](https://mlsanity.com/paper/2108.11986/) (2021)
- [That Label's Got Style: Handling Label Style Bias for Uncertain Image Segmentation](https://mlsanity.com/paper/2303.15850/) (2023)
- [On the Optimal Combination of Cross-Entropy and Soft Dice Losses for Lesion Segmentation with Out-of-Distribution Robustness](https://mlsanity.com/paper/2209.06078/) (2022)
- [Laplacian Segmentation Networks Improve Epistemic Uncertainty Quantification](https://mlsanity.com/paper/2303.13123/) (2023)

## Abstract (arXiv)

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.