Summary of Statistical and Computational Guarantees Of Kernel Max-sliced Wasserstein Distances, by Jie Wang and March Boedihardjo and Yao Xie
Statistical and Computational Guarantees of Kernel Max-Sliced Wasserstein Distances
by Jie Wang, March Boedihardjo, Yao Xie
First submitted to arxiv on: 24 May 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Computational Complexity (cs.CC); 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 paper proposes a novel approach to optimal transport, called kernel max-sliced (KMS) Wasserstein distance, which reduces high-dimensional data into 1 dimension before computing the Wasserstein distance. This method is developed to overcome the curse of dimensionality and provides sharp finite-sample guarantees for the KMS p-Wasserstein distance between two empirical distributions. The authors also show that computing the KMS 2-Wasserstein distance is NP-hard, but propose a semidefinite relaxation (SDR) formulation that can be solved efficiently in polynomial time. This method is demonstrated to perform well in high-dimensional two-sample testing. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper finds a new way to make optimal transport work better with big data. Right now, it can get stuck when dealing with high-dimensional data and low-dimensional structures. The authors create a special kind of Wasserstein distance that reduces the dimensionality first, making it more efficient. They also show that some calculations are too hard to do exactly, but provide an easier way to solve them approximately. This new method is tested on big datasets and seems to work well. |
