Summary of Tree-sliced Wasserstein Distance on a System Of Lines, by Viet-hoang Tran et al.
Tree-Sliced Wasserstein Distance on a System of Lines
by Viet-Hoang Tran, Trang Pham, Tho Tran, Tam Le, Tan M. Nguyen
First submitted to arxiv on: 19 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Machine Learning (stat.ML)
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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 Tree-Sliced Wasserstein distance on a System of Lines (TSW-SL), which combines the benefits of Sliced Wasserstein (SW) and Tree-sliced Wasserstein (TSW). TSW is an Optimal Transport (OT) method for probability measures where the ground cost is a tree metric, offering higher degrees of freedom than SW. However, existing methods rely heavily on given supports, limiting their adaptability to new supports. TSW-SL addresses this issue by projecting measures onto a system of lines using a variant of the Radon Transform, then leveraging Tree Wassenstein (TW) for efficient distance computation. The paper demonstrates the advantages of TSW-SL over SW and TSW through experiments in gradient flows, image style transfer, and generative models. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper finds a new way to compare two groups of things, like images or numbers. It uses something called Tree-Sliced Wasserstein distance on a System of Lines (TSW-SL). This method is better than some other methods because it can adapt to different situations and doesn’t lose important information about the groups being compared. The authors tested TSW-SL with different types of data, like images or numbers, and found that it worked well in all cases. |
Keywords
* Artificial intelligence * Probability * Style transfer
