Summary of Relative-translation Invariant Wasserstein Distance, by Binshuai Wang et al.
Relative-Translation Invariant Wasserstein Distance
by Binshuai Wang, Qiwei Di, Ming Yin, Mengdi Wang, Quanquan Gu, Peng Wei
First submitted to arxiv on: 4 Sep 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: 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 A new family of distances called relative-translation invariant Wasserstein distances (RW_p) is introduced for measuring the similarity of two probability distributions under distribution shift. These distances generalize the classical optimal transport model and are shown to be real distance metrics defined on the quotient set P_p(R^n)/~ and invariant to distribution translations. The RW_2 distance, in particular, enjoys decomposability, translation-invariance, and a Pythagorean relationship with the classical quadratic Wasserstein distance (W_2). This allows for an explanation of distribution shift measured by W_2 distance in the bias-variance perspective. A variant of the Sinkhorn algorithm, named RW_2 Sinkhorn algorithm, is proposed for efficiently calculating RW_2 distance and coupling solutions, as well as W_2 distance. The algorithm’s numerical stability and time complexity are analyzed, and experimental results validate its performance with three experiments demonstrating the effectiveness of using RW_2 under distribution shift in digits recognition and similar thunderstorm detection. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This research introduces a new way to measure how different two probability distributions are when one has shifted or changed. They call this measurement “relative-translation invariant Wasserstein distances” or RW_p for short. This helps us understand why some things might be harder to recognize or predict because of these changes. The researchers also came up with a new algorithm that makes it faster and more efficient to calculate this distance, which they tested on real-world data like recognizing numbers and detecting thunderstorms. |
Keywords
» Artificial intelligence » Probability » Translation
