Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2509.11532 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915494355795968 |
|---|---|
| author | La Vecchia, Davide Liu, Hang |
| author_facet | La Vecchia, Davide Liu, Hang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11532 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | E-ROBOT: a dimension-free method for robust statistics and machine learning via Schrödinger bridge La Vecchia, Davide Liu, Hang Machine Learning 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. |
| title | E-ROBOT: a dimension-free method for robust statistics and machine learning via Schrödinger bridge |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2509.11532 |