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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.01310 |
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| _version_ | 1866908849086136320 |
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| author | Tarasov, Roman Mokrov, Petr Gazdieva, Milena Burnaev, Evgeny Korotin, Alexander |
| author_facet | Tarasov, Roman Mokrov, Petr Gazdieva, Milena Burnaev, Evgeny Korotin, Alexander |
| contents | Neural network-based optimal transport (OT) is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain translation, image super-resolution, computational biology and others. Among the existing OT approaches, of considerable interest are adversarial minimax solvers based on semi-dual formulations of OT problems. While promising, these methods lack theoretical investigation from a statistical learning perspective. Our work fills this gap by establishing upper bounds on the generalization error of an approximate OT map recovered by the minimax quadratic OT solver. Importantly, the bounds we derive depend solely on some standard statistical and mathematical properties of the considered functional classes (neural nets). While our analysis focuses on the quadratic OT, we believe that similar bounds could be derived for general OT case, paving the promising direction for future research. Our experimental illustrations are available online https://github.com/milenagazdieva/StatOT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01310 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers Tarasov, Roman Mokrov, Petr Gazdieva, Milena Burnaev, Evgeny Korotin, Alexander Machine Learning Artificial Intelligence Neural network-based optimal transport (OT) is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain translation, image super-resolution, computational biology and others. Among the existing OT approaches, of considerable interest are adversarial minimax solvers based on semi-dual formulations of OT problems. While promising, these methods lack theoretical investigation from a statistical learning perspective. Our work fills this gap by establishing upper bounds on the generalization error of an approximate OT map recovered by the minimax quadratic OT solver. Importantly, the bounds we derive depend solely on some standard statistical and mathematical properties of the considered functional classes (neural nets). While our analysis focuses on the quadratic OT, we believe that similar bounds could be derived for general OT case, paving the promising direction for future research. Our experimental illustrations are available online https://github.com/milenagazdieva/StatOT. |
| title | A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2502.01310 |