Collaborative Research: Statistical Optimal Transport in High Dimensional Mixtures

合作研究：高维混合物中的统计最优传输

• 批准号: 2210583
• 负责人: Jonathan Niles-Weed
• 金额: $ 17.5万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2210583&HistoricalAwards=false
• 关键词: Collaborative; Research; Statistical; Optimal; Transport

This project studies high-dimensional mixture models, a class of statistical models that can be used to analyze data arising in linguistics, computational biology, and particle physics. This research project aims to define a new measure of distance between distributions that measures their similarity with respect to a mixture model and offers a principled way to compare, transform, and analyze high-dimensional data sets. As part of this project, the investigators will develop fast algorithms for estimating this distance and theoretical guarantees allowing this distance to be used for statistical inference.Specifically, this project defines a sketched Wasserstein distance (SWD) and will develop its computational and statistical properties. The primary aims are to establish duality relations for this distance, develop computationally feasible estimators for SWD using both primal and dual formulations, and to study the rates of convergence of the new estimators. In addition, the research aims to develop lower bounds to establish the rate optimality of these estimators and establish distributional limits to allow for the construction of asymptotically valid confidence intervals. These tools will be applied to data in text analysis, systems biology, and high-energy physics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目研究高维混合模型，这是一类统计模型，可用于分析语言学、计算生物学和粒子物理学中产生的数据。该研究项目旨在定义一种新的分布之间的距离度量，以测量它们相对于混合模型的相似性，并提供一种比较、转换和分析高维数据集的原则方法。作为该项目的一部分，研究人员将开发快速算法来估计该距离，并提供理论保证，使该距离可用于统计推断。具体来说，该项目定义了草图 Wasserstein 距离 (SWD)，并将开发其计算和统计特性。主要目标是建立该距离的对偶关系，使用原始公式和对偶公式开发计算上可行的 SWD 估计器，并研究新估计器的收敛率。此外，该研究旨在开发下限来建立这些估计量的速率最优性，并建立分布限制以允许构建渐近有效的置信区间。这些工具将应用于文本分析、系统生物学和高能物理学中的数据。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。