Statistical Estimation from Decoupled Data

根据解耦数据进行统计估计

基本信息

批准号：
2015291
负责人：
Jonathan Niles-Weed
金额：
$ 25万
依托单位：
New York University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-07-01 至 2023-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2015291&HistoricalAwards=false
关键词：
Statistical Estimation Decoupled Data

项目摘要

Modern statistics is defined by the fact that a great deal more data is available to practitioners than ever before. This is particularly the case in the sciences, where advances in experimental methodology across fields such as biology, chemistry, and physics have led to an explosion of different types of data, collected by different measurement apparatuses at potentially different times. Moreover, it may be difficult or impossible to connect data points from different experiments. For example, a chemist may apply two different measurement techniques to the same batch of molecules to obtain high-quality data about the whole batch, but it may be challenging to track the identities of particular molecules between measurements. The statistician who wishes to make the best possible inferences is faced with the difficult problem of how to integrate the data from different sources to conduct a unified analysis. Despite the ubiquity of this problem, rigorous statistical analyses of procedures designed to work with decoupled data are rare. The main goal of this project is to develop new tools for performing estimation tasks with decoupled data and to establish the fundamental limits of such techniques. This project will have impact on scientific and statistical methodology in both research and industrial settings.The graduate student support will be used on interdisciplinary research and writing codes. The project will investigate optimal rates of estimation for regression problems given access to decoupled data, and to establish potential trade-offs. Several intermediate regimes will be considered, for example, where the experimenter has access to many independent batches of shuffled data or to data with partial coupling information. This project will quantify the statistical price for learning with decoupled data via tight minimax bounds. This research is also aimed at establishing when minimax statistical procedures can be made computationally efficient, and investigating the possible presence of information theoretic-computational gaps in optimal rates of estimation.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.

现代统计数据是由以下事实定义的：从业者比以往任何时候都可以使用更多的数据。在科学中尤其如此，在这种情况下，跨生物学，化学和物理学等领域的实验方法的进步导致了不同类型的数据的爆炸，这是通过潜在不同时间的不同测量机构收集的。此外，从不同实验中连接数据点可能很困难或不可能。例如，化学家可能对同一批分子应用两种不同的测量技术来获得有关整个批次的高质量数据，但是跟踪测量之间特定分子的身份可能具有挑战性。希望做出最佳推论的统计学家面临着如何整合来自不同来源的数据以进行统一分析的困难问题。尽管这个问题无处不在，但旨在与脱钩数据一起使用的程序进行了严格的统计分析。该项目的主要目标是开发新的工具，用于使用脱钩数据执行估算任务，并建立此类技术的基本限制。该项目将对研究和工业环境中的科学和统计方法产生影响。研究生的支持将用于跨学科研究和写作代码。该项目将调查访问脱钩数据并建立潜在权衡的回归问题的最佳估计率。例如，将考虑几个中级制度，例如，实验者可以访问许多独立的洗牌数据或带有部分耦合信息的数据。该项目将通过紧密的最小界限使用解耦数据来量化学习的统计价格。这项研究还旨在确定最小值统计程序可以在计算上有效，并在最佳估计速率中调查信息理论上的差距的可能存在。该奖项反映了NSF的法定任务，并认为通过使用该基金会的知识分子和更广泛的影响来审查Criteria，通过评估来进行评估。