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About this paper
Cheongjae Jang, Jonghyun Won, Soyeon Jun, Chun Kee Chung, Keehyoung Joo, Yung-Kyun Noh
An analytical framework demonstrates how the one-dimensional Wasserstein distance with finite samples effectively encodes both rate and support differences in probability distributions. This metric enhanced stimulus classification for retinal ganglion cells and revealed biochemical properties in amino acid contact frequencies, showing its practical utility in capturing distinct data patterns.
Key insights
- The one-dimensional Wasserstein distance can explicitly and analytically capture pointwise density differences, or rate information, even with finite samples.
- Wasserstein distance effectively harmonizes both rate and support differences, integrating these distinct types of information within a single metric.
- The analytical characterization of 1D Wasserstein distance provides a crucial theoretical foundation for understanding and applying its higher-dimensional variants, such as sliced Wasserstein distances.
Summary by alphaXiv.
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