{"ID":2870714,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.11532","arxiv_id":"2509.11532","title":"E-ROBOT: a dimension-free method for robust statistics and machine learning via Schrödinger bridge","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 $\\overline{W}_{\\varepsilon,λ}$, where the parameter $λ$ controls robustness and $\\varepsilon$ governs the regularization strength. Letting $n\\in \\mathbb{N}$ denote the sample size, a central theoretical contribution is establishing that the sample complexity of $\\overline{W}_{\\varepsilon,λ}$ is $\\mathcal{O}(n^{-1/2})$, thereby avoiding the curse of dimensionality that plagues standard ROBOT. This dimension-free property unlocks the use of $\\overline{W}_{\\varepsilon,λ}$ 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 (\\texttt{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.","short_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...","url_abs":"https://arxiv.org/abs/2509.11532","url_pdf":"https://arxiv.org/pdf/2509.11532v1","authors":"[\"Davide La Vecchia\",\"Hang Liu\"]","published":"2025-09-15T02:49:04Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\"]","methods":"[]","has_code":false}