# Partial Wasserstein and Maximum Mean Discrepancy distances for bridging the gap between outlier detection and drift detection

arXiv: https://arxiv.org/abs/2106.12893 · HTML: https://mlsanity.com/paper/2106.12893/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 12 references that are in the map.
- First posted on arXiv 9 Jun 2021.

## Builds on (most cited first, 6 of 6)

- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Failing Loudly: An Empirical Study of Methods for Detecting Dataset Shift](https://mlsanity.com/paper/1810.11953/) (2018)
- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [Subspace Robust Wasserstein Distances](https://mlsanity.com/paper/1901.08949/) (2019)

## Built on by (most cited first, 3 of 3)

- [Representative, Informative, and De-Amplifying: Requirements for Robust Bayesian Active Learning under Model Misspecification](https://mlsanity.com/paper/2506.07805/) (2025)
- [Frouros: A Python library for drift detection in machine learning systems](https://mlsanity.com/paper/2208.06868/) (2022)
- [Learning to Land Anywhere: Transferable Generative Models for Aircraft Trajectories](https://mlsanity.com/paper/2511.04155/) (2025)

## Abstract (arXiv)

With the rise of machine learning and deep learning based applications in practice, monitoring, i.e. verifying that these operate within specification, has become an important practical problem. An important aspect of this monitoring is to check whether the inputs (or intermediates) have strayed from the distribution they were validated for, which can void the performance assurances obtained during testing. There are two common approaches for this. The, perhaps, more classical one is outlier detection or novelty detection, where, for a single input we ask whether it is an outlier, i.e. exceedingly unlikely to have originated from a reference distribution. The second, perhaps more recent approach, is to consider a larger number of inputs and compare its distribution to a reference distribution (e.g. sampled during testing). This is done under the label drift detection. In this work, we bridge the gap between outlier detection and drift detection through comparing a given number of inputs to an automatically chosen part of the reference distribution.