Summary of Monge-kantorovich Fitting with Sobolev Budgets, by Forest Kobayashi et al.
Monge-Kantorovich Fitting With Sobolev Budgets
by Forest Kobayashi, Jonathan Hayase, Young-Heon Kim
First submitted to arxiv on: 25 Sep 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Analysis of PDEs (math.AP)
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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 paper explores the problem of approximating an n-dimensional probability measure using a measure with support parametrized by a function f. The approximation is evaluated using the Monge-Kantorovich p-cost, and the complexity of the approximation is constrained by bounding the Sobolev norm of f. The approach can be reformulated as minimizing a functional under a constraint on the Sobolev budget. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper helps us find the best way to approximate an n-dimensional probability measure using another measure with a support that depends on a function. It uses a special cost called the Monge-Kantorovich p-cost to see how well the approximation works, and it makes sure not to use too much complexity by controlling the Sobolev norm of the function. This helps us understand how to solve this problem in a way that’s efficient and effective. |
Keywords
* Artificial intelligence * Probability
