EMBEDDING DISTRIBUTIONAL DATA

• 成果类型: Article
• 署名作者: Arias-Castro, Ery; Qiao, Wanli
• 署名单位: University of California System; University of California San Diego; University of California System; University of California San Diego; George Mason University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2471
• 发表日期: 2025
• 页码: 615-646
• 关键词: statistical variables; divergence estimation; sample; SPACE; distance; MODEL; INFORMATION; regression; complex; root

摘要

We adapt concepts, methodology, and theory originally developed in the areas of multidimensional scaling and dimensionality reduction for Euclidean data to be applicable to distributional data. We focus on classical scaling and Isomap-prototypical methods that have played important roles in these areas-and showcase their use in the context of distributional data analysis. In the process, we highlight the crucial role that the ambient metric plays.