Papers › Wasserstein Spatial Depth
Wasserstein Spatial Depth
François Bachoc, Alberto González-Sanz, Jean-Michel Loubes, Yisha Yao
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the distinct geometry and unique properties of Wasserstein spaces pose challenges to the application of conventional statistical tools, which are primarily designed for Euclidean spaces. Consequently, adapting and developing new methodologies for analysis within Wasserstein spaces has become essential. The space of distributions on ℝᵈ with d>1 is not linear, and "mimic" the geometry of a Riemannian manifold. In this paper, we extend the concept of statistical depth to distribution-valued data, introducing the notion of Wasserstein spatial depth. This new measure provides a way to rank and order distributions, enabling the development of order-based clustering techniques and inferential tools. We show that Wasserstein spatial depth (WSD) preserves critical properties of conventional statistical depths, notably, ranging within [0,1], transformation and geodesic invariance, vanishing at infinity, reaching a maximum at the geometric median, and continuity. Regarding robustness, we characterize the breakdown points of the empirical depth regions and the influence function of the WSD. Additionally, the population WSD has a straightforward plug-in estimator based on sampled empirical distributions. We establish the estimator's consistency and asymptotic normality. We also provide a two-sample test for populations of distributions based on the WSD. Finally, extensive simulations and a real-data application showcase the practical efficacy of the WSD.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections