Differentiable Cost-Parameterized Monge Map Estimators
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914833059807232 |
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| author | Howard, Samuel Deligiannidis, George Rebeschini, Patrick Thornton, James |
| author_facet | Howard, Samuel Deligiannidis, George Rebeschini, Patrick Thornton, James |
| contents | Within the field of optimal transport (OT), the choice of ground cost is crucial to ensuring that the optimality of a transport map corresponds to usefulness in real-world applications. It is therefore desirable to use known information to tailor cost functions and hence learn OT maps which are adapted to the problem at hand. By considering a class of neural ground costs whose Monge maps have a known form, we construct a differentiable Monge map estimator which can be optimized to be consistent with known information about an OT map. In doing so, we simultaneously learn both an OT map estimator and a corresponding adapted cost function. Through suitable choices of loss function, our method provides a general approach for incorporating prior information about the Monge map itself when learning adapted OT maps and cost functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_08399 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differentiable Cost-Parameterized Monge Map Estimators Howard, Samuel Deligiannidis, George Rebeschini, Patrick Thornton, James Machine Learning Within the field of optimal transport (OT), the choice of ground cost is crucial to ensuring that the optimality of a transport map corresponds to usefulness in real-world applications. It is therefore desirable to use known information to tailor cost functions and hence learn OT maps which are adapted to the problem at hand. By considering a class of neural ground costs whose Monge maps have a known form, we construct a differentiable Monge map estimator which can be optimized to be consistent with known information about an OT map. In doing so, we simultaneously learn both an OT map estimator and a corresponding adapted cost function. Through suitable choices of loss function, our method provides a general approach for incorporating prior information about the Monge map itself when learning adapted OT maps and cost functions. |
| title | Differentiable Cost-Parameterized Monge Map Estimators |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2406.08399 |