Statistical Design, Sampling, and Analysis for Large Scale Experiments

在大数据范式下，即使是受控实验也可以变得大规模，因为样本量很大，输入变量的维度很高。这种大数据问题挑战了许多统计方法，并显著增加了估计和推理的计算量。在这个项目中，PI专注于大型实验的具体实例，并在实验设计、采样和分析方面发展了一套新的理论和方法。这项研究包括两个主要部分。在第一部分中，PI侧重于包含大量协变量的实验类型。例如，在临床试验中，协变量可以是患者丰富的病史。应该如何将治疗设置分配给每个患者？PI通过一个通用的实验设计框架提供了答案，以便在不受协变量影响的情况下准确地估计处理效果。在第二部分中，PI重点介绍了最流行的统计学习工具之一--高斯过程(GP)回归。对于分析大规模实验，如气候模型模拟，所需的计算是令人望而却步的。PI开发了一个降维框架和一种主动学习方法，显著提高了GP模型的效率和精度。在第1-3部分中，PI介绍了一种新的基于差异的设计，以实现协变量平衡的实验与大维度的协变量。差异标准还具有吸引人的理论性质，导致对包括治疗效应和协变量效应在内的参数的更准确估计。开发了离线和在线实验的优化设计算法。在第四部分中，PI提出了一种新的降维方法，为GP模型寻找低维核函数的最优凸组合。结果表明，该方法是一种计算量较小且对某些类型的基本函数有较高精度的近似方法。第五部分提出了一种基于广义库克距离的GP回归主动学习方法。它比标准的随机抽样方法效率更高。本研究思路新颖，理论严谨，具有实用价值，将为实验领域的统计设计和分析开辟新的方向。PI有一个详细的教育计划，以此项目的研究成果为基础开发新的课程模块、教程和研讨会。研究成果适用于需要大规模数据收集和分析的各种科学、工程、医学和其他领域。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。

In the big data paradigm, even the controlled experiments can become large-scale, in the sense that the sample size is massive, and the dimension of the input variables is high. Such "big data" problem challenges many statistical approaches and significantly increases the amount of computation in estimation and inference. In this project, the PI focuses on specific instances of large-scale experiments and develops a set of novel theories and methodologies on experimental design, sampling, and analysis. The research has two major parts. In Part 1, the PI focuses on the type of experiments that contains a large dimension of covariate variables. For example, in a clinical trial, the covariates can be patients' rich medical history. How should the treatment settings be assigned to each patient? The PI provides the answer through a general experimental design framework so that the treatment effects are estimated accurately despite the influence of the covariates. In Part 2, the PI focuses on the Gaussian Process (GP) regression, one of the most popular statistical learning tools. The computation required is prohibitive for analyzing large-scale experiments such as the climate model simulations. The PI develops a dimension reduction framework and an active learning method that significantly improves the efficiency and accuracy of the GP model.Three major methodologies are considered. In Parts 1-3, the PI introduces a new discrepancy-based design to achieve covariate balance for experiments with a large dimension of covariates. The discrepancy criterion also has appealing theoretical properties that lead to a more accurate estimation of the parameters including both treatment effects and covariates' effects. Optimal design algorithms are developed for both offline and online experiments. In Part 4, the PI develops a novel dimension reduction method that finds the optimal convex combination of low-dimension kernel functions for the GP model. It is shown that the proposed method is a significantly less computational and more accurate approximation of certain types of underlying functions. In Part 5, an active learning method based on the generalized Cook's Distance is developed for the GP regression. It is more efficient than the standard random sampling method. The research is novel in ideas, rigorous in theories, and useful in practice, and will open new directions in the statistical design and analysis of experiments area. The PI has a detailed education plan to develop new course modules, tutorials, and workshops based on the research products from this project. The research outcomes are readily applicable to a variety of scientific, engineering, medicine and other fields where large-scale data collection and analysis are demanded.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.