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.

现代统计学的定义是，从业者可以获得比以往更多的数据。在科学领域尤其如此，生物学、化学和物理学等领域实验方法的进步导致不同类型的数据激增，这些数据由不同的测量设备在不同的时间收集。此外，连接来自不同实验的数据点可能很困难或不可能。例如，化学家可以对同一批次的分子应用两种不同的测量技术，以获得有关整个批次的高质量数据，但跟踪测量之间特定分子的身份可能具有挑战性。希望做出尽可能最佳推论的统计学家面临着如何整合不同来源的数据以进行统一分析的难题。尽管这个问题普遍存在，但对旨在处理解耦数据的程序进行严格的统计分析却很少。该项目的主要目标是开发新工具，用于使用解耦数据执行估计任务，并确定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编写代码。该项目将研究在获得解耦数据的情况下回归问题的最佳估计率，并建立潜在的权衡。例如，将考虑几种中间方案，其中实验者可以访问许多独立批次的混洗数据或具有部分耦合信息的数据。该项目将通过严格的极小极大界限量化解耦数据学习的统计成本。这项研究还旨在确定何时可以提高极小极大统计程序的计算效率，并调查最佳估计率中可能存在的信息论计算差距。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。