E-ROBOT: a dimension-free method for robust statistics and machine learning via Schrödinger bridge.
- 1Geneva School of Economics and Management, University of Geneva, Bld. du Pont d'Arve, Geneva, CH-1211 Switzerland.
- 2Department of Statistics and Finance, School of Management, University of Science and Technology of China, Jinzhai Rd, Hefei, 230026 Anhui Province China.
Abstract
We propose the Entropic-regularized Robust Optimal Transport (E-ROBOT) framework, a novel method that combines the robustness of ROBOT with the computational and statistical benefits of entropic regularization. We show that, rooted in the Schrödinger bridge problem theory, E-ROBOT defines the robust Sinkhorn divergence W¯ε,λ , where the parameter λ controls robustness and ε governs the regularization strength. Letting n∈N denote the sample size, a central theoretical contribution is establishing that the sample complexity of W¯ε,λ is O(n-1/2) , thereby avoiding the curse of dimensionality that plagues standard ROBOT. This dimension-free property unlocks the use of W¯ε,λ as a loss function in large-dimensional statistical and machine learning tasks. With this regard, we demonstrate its utility through four applications: goodness-of-fit testing; computation of barycenters for corrupted 2D and 3D shapes; definition of gradient flows; and image colour transfer. From the computation standpoint, a perk of our novel method is that it can be easily implemented by modifying existing (Python) routines. From the theoretical standpoint, our work opens the door to many research directions in statistics and machine learning: we discuss some of them.Supplementary information
The online version contains supplementary material available at https://doi.org/10.1007/s11222-026-10914-9.
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BibTeX
@article{vecchia2026erobot,
title = {{E-ROBOT: a dimension-free method for robust statistics and machine learning via Schrödinger bridge.}},
author = {Davide La Vecchia and Hang Liu},
journal = {Statistics and computing},
year = {2026},
month = jun,
doi = {10.1007/s11222-026-10914-9},
url = {https://europepmc.org/article/MED/42908772},
note = {CC BY},
}
RIS
TY - JOUR
TI - E-ROBOT: a dimension-free method for robust statistics and machine learning via Schrödinger bridge.
AU - Davide La Vecchia
AU - Hang Liu
PY - 2026
DA - 2026/06/06
JO - Statistics and computing
DO - 10.1007/s11222-026-10914-9
UR - https://europepmc.org/article/MED/42908772
AB - We propose the Entropic-regularized Robust Optimal Transport (E-ROBOT) framework, a novel method that combines the robustness of ROBOT with the computational and statistical benefits of entropic regularization. We show that, rooted in the Schrödinger bridge problem theory, E-ROBOT defines the robust Sinkhorn divergence W¯ε,λ , where the parameter λ controls robustness and ε governs the regularization strength. Letting n∈N denote the sample size, a central theoretical contribution is establishing that the sample complexity of W¯ε,λ is O(n-1/2) , thereby avoiding the curse of dimensionality that plagues standard ROBOT. This dimension-free property unlocks the use of W¯ε,λ as a loss function in large-dimensional statistical and machine learning tasks. With this regard, we demonstrate its utility through four applications: goodness-of-fit testing; computation of barycenters for corrupted 2D and 3D shapes; definition of gradient flows; and image colour transfer. From the computation standpoint, a perk of our novel method is that it can be easily implemented by modifying existing (Python) routines. From the theoretical standpoint, our work opens the door to many research directions in statistics and machine learning: we discuss some of them.Supplementary information The online version contains supplementary material available at https://doi.org/10.1007/s11222-026-10914-9.
SN - 0960-3174
ER -