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Explanation of Variability through Optimal Transport

通过最佳传输解释可变性

基本信息

批准号：
1715753
负责人：
Esteban Tabak
金额：
$ 44.56万
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：
2017
资助国家：
美国
起止时间：
2017-08-01 至 2020-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1715753&HistoricalAwards=false
关键词：
Explanation Variability through Optimal Transport

项目摘要

1715753Tabak The investigator develops a methodology for the explanation of variability in data attributable to known and unknown external factors. This has applications in all data-intensive fields, including public health, economics, and environmental studies. It provides a natural tool for personalized medicine, as it can both filter from data the influence of each patient's characteristics, such as age and sex, and particularize the predictions to account for the specifics of each patient. It also permits the analysis of meteorological data taken at different locations and times and with different instruments, and of unstructured time series depending on known and unknown external factors. Graduate and postdoctoral students participate in the work of the project. The problems of amalgamating datasets and removing external factors of variability find a very natural formulation in an extension of the mathematical theory of optimal transport: both problems concern normalizing (i.e. transporting) the original data so that no signal is left that points to the dataset of provenance or the values of the confounding variables. On the other hand, the transport needs to be optimized, minimizing the removal of variability associated to other sources. This project extends the theory of optimal transport to handle these problems. The extensions include problems such as finding the barycenter of a continuum of probability densities of which only a finite amount of samples are known. Graduate and postdoctoral students participate in the work of the project.

小行星1715753 研究者开发一种方法来解释已知和未知外部因素导致的数据变异性。这在所有数据密集型领域都有应用，包括公共卫生，经济学和环境研究。它为个性化医疗提供了一种天然的工具，因为它既可以从数据中过滤每个患者特征（例如年龄和性别）的影响，又可以详细说明预测以说明每个患者的具体情况。它还允许分析在不同地点和时间用不同仪器获得的气象数据，以及根据已知和未知的外部因素分析非结构化时间序列。研究生和博士后学生参与该项目的工作。合并数据集和去除可变性的外部因素的问题在最优传输的数学理论的扩展中找到了一个非常自然的公式：这两个问题都涉及将原始数据标准化（即传输），以便没有信号指向来源数据集或混淆变量的值。另一方面，需要优化传输，最大限度地减少与其他来源相关的可变性的去除。这个项目扩展了最优运输理论来处理这些问题。扩展包括的问题，如找到一个连续的概率密度的重心，其中只有有限数量的样本是已知的。研究生和博士后学生参与该项目的工作。