Summary of (de)-regularized Maximum Mean Discrepancy Gradient Flow, by Zonghao Chen et al.
(De)-regularized Maximum Mean Discrepancy Gradient Flow
by Zonghao Chen, Aratrika Mustafi, Pierre Glaser, Anna Korba, Arthur Gretton, Bharath K. Sriperumbudur
First submitted to arxiv on: 23 Sep 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 proposed (de)-regularization of Maximum Mean Discrepancy (DrMMD) and its Wasserstein gradient flow offers an improvement over existing methods. The novel approach ensures near-global convergence for a broad range of targets in both continuous and discrete time, while also providing a tractable numerical implementation using only samples. This is achieved by leveraging the connection between DrMMD and the χ2-divergence, as well as treating DrMMD as MMD with a de-regularized kernel. The adaptive de-regularization schedule optimizes the trade-off between discretization errors and deviations from the χ2 regime. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The DrMMD flow is an innovative way to transport samples from source to target distributions using only target samples. This method ensures convergence for a wide range of targets, both in continuous and discrete time. The algorithm uses samples alone to implement the flow in closed form. The potential applications of this technique are showcased through several numerical experiments. |
Keywords
* Artificial intelligence * Regularization
