# On Robust Cross Domain Alignment

arXiv: https://arxiv.org/abs/2412.15861 · HTML: https://mlsanity.com/paper/2412.15861/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 67 references that are in the map.
- First posted on arXiv 20 Dec 2024.

## Builds on (most cited first, 9 of 9)

- [Generalized Dimension Reduction Using Semi-Relaxed Gromov-Wasserstein Distance](https://mlsanity.com/paper/2405.15959/) (2024)
- [Lower Complexity Adaptation for Empirical Entropic Optimal Transport](https://mlsanity.com/paper/2306.13580/) (2023)
- [The Z-Gromov-Wasserstein Distance](https://mlsanity.com/paper/2408.08233/) (2024)
- [Robust Estimation under the Wasserstein Distance](https://mlsanity.com/paper/2302.01237/) (2023)
- [Partial Gromov-Wasserstein Metric](https://mlsanity.com/paper/2402.03664/) (2024)
- [Entropic Gromov-Wasserstein Distances: Stability and Algorithms](https://mlsanity.com/paper/2306.00182/) (2023)
- [Active Linear Regression for ℓp Norms and Beyond](https://mlsanity.com/paper/2111.04888/) (2021)
- [Inference via robust optimal transportation: theory and methods](https://mlsanity.com/paper/2301.06297/) (2023)
- [Concurrent Density Estimation with Wasserstein Autoencoders: Some Statistical Insights](https://mlsanity.com/paper/2312.06591/) (2023)

## Abstract (arXiv)

The Gromov-Wasserstein (GW) distance is an effective measure of alignment between distributions supported on distinct ambient spaces. Calculating essentially the mutual departure from isometry, it has found vast usage in domain translation and network analysis. It has long been shown to be vulnerable to contamination in the underlying measures. All efforts to introduce robustness in GW have been inspired by similar techniques in optimal transport (OT), which predominantly advocate partial mass transport or unbalancing. In contrast, the cross-domain alignment problem being fundamentally different from OT, demands specific solutions to tackle diverse applications and contamination regimes. Deriving from robust statistics, we discuss three contextually novel techniques to robustify GW and its variants. For each method, we explore metric properties and robustness guarantees along with their co-dependencies and individual relations with the GW distance. For a comprehensive view, we empirically validate their superior resilience to contamination under real machine learning tasks against state-of-the-art methods.