Statistical Estimation from Decoupled Data

现代统计学的定义是，从业者可以获得的数据比以往任何时候都多。在科学领域尤其如此，在生物、化学和物理等领域，实验方法学的进步导致了不同类型的数据的爆炸性增长，这些数据由不同的测量仪器在潜在的不同时间收集。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，化学家可能会对同一批分子应用两种不同的测量技术，以获得关于整批分子的高质量数据，但在两次测量之间追踪特定分子的身份可能是具有挑战性的。想要做出最佳推断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难题。尽管这个问题无处不在，但对处理分离数据的程序进行严格的统计分析却很少见。该项目的主要目标是开发新的工具，用于使用分离的数据执行估计任务，并确定这种技术的基本限制。这个项目将在研究和工业环境中对科学和统计方法产生影响。研究生资助将用于跨学科研究和编写代码。该项目将调查在获得分离数据的情况下回归问题的最佳估计率，并建立潜在的权衡。将考虑几种中间机制，例如，当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时。这个项目将通过严格的极小极大界来量化使用解耦数据进行学习的统计代价。这项研究还旨在确定何时可以使极小极大统计程序在计算上有效，并调查最优估计率中可能存在的信息理论-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优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.