Summary of Differentiable Cost-parameterized Monge Map Estimators, by Samuel Howard et al.
Differentiable Cost-Parameterized Monge Map Estimators
by Samuel Howard, George Deligiannidis, Patrick Rebeschini, James Thornton
First submitted to arxiv on: 12 Jun 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The abstract proposes a novel approach to optimal transport (OT) by constructing a differentiable Monge map estimator that can be optimized with prior knowledge about an OT map. This method simultaneously learns both an OT map estimator and a corresponding adapted cost function, allowing for the incorporation of prior information about the Monge map itself when learning adapted OT maps and cost functions. The approach uses neural ground costs whose Monge maps have a known form, enabling the adaptation of OT maps to real-world applications. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper explores ways to improve optimal transport (OT) by tailoring the cost function to suit specific problems. It does this by creating a new way to estimate OT maps and their corresponding cost functions. This method can be used to incorporate prior knowledge about an OT map, making it more useful for real-world applications. |
