From Approximate to Exact Designs with Applications to Big Data

在许多研究领域，如生物科学、健康科学、社会科学、工程学、营销学和教育学，实验设计是科学过程的组成部分，对社会有直接影响。精心选择的设计有助于以最低的成本收集数据，最大限度地为感兴趣的科学问题提供信息。许多科学研究允许重复使用概念单元，因此为这些问题开发优化设计的工具具有巨大的潜在影响。特别是在大数据领域，现有的实验设计方法有很大的改进空间，本研究项目中正在开发的工具和概念有可能在不增加计算成本的情况下显著获得信息。该项目的结果将通过易于使用的软件提供给其他领域的研究人员，这些软件实现了将要开发的算法。研究生将被培养成实验设计方面的研究人员。这个项目的目的是在理解和了解最优实验设计方面取得重大飞跃。最近在该领域的工作对最优交叉设计和任意给定协方差结构和设计大小配置的干扰模型的设计的推进产生了重大影响。然而，这些结果在很大程度上仅限于相对简单的模型的近似设计。虽然这些结果本身就很重要，但该项目将扩展方法和工具，以实现为更广泛的实用模型得出准确设计的最终目标。其结果将是我们集体设计工具箱中亟需的补充。最重要的是，该项目将超越设计领域，将从实验设计到大数据中出现的欠抽样问题的工具和想法应用到正在考虑的统计和机器学习方法中。初步结果表明，现在是采取这些具有挑战性但至关重要的步骤的好时机。

Design of experiments is an integral part of the scientific process in many areas of research with a direct impact on society, such as the biological sciences, the health sciences, the social sciences, engineering, marketing, and education. A well-chosen design facilitates the collection of data that, at a minimum cost, maximizes the information for the scientific questions of interest. Many scientific studies allow for repeated use of conceptual units, so that developing tools for optimal design for these problems has great potential impact. Particularly in the realm of big data, there is much room for improvement of existing methods for design of experiments, and the tools and concepts under development in this research project have potential to lead to significant gain of information without increasing computational cost. Results from the project will be made available to researchers in other areas through easy-to-use software that implements the algorithms to be developed. Graduate students will be trained to become researchers in design of experiments. This project aims to result in a major leap forward in understanding and knowledge of optimal design of experiments. Recent work in the field has had a significant impact on the advancement of optimal crossover designs and designs for interference models for arbitrarily given covariance structures and design size configurations. However, these results have for the most part been limited to approximate designs for relatively simple models. While these results are arguably important in their own right, this project will extend methods and tools to achieve the ultimate goal of deriving exact designs for a wider spectrum of practical models. The results will be a much needed addition to our collective design toolbox. Most importantly, this project will go beyond the territory of design and apply the tools and ideas from design of experiments to subsampling problems emerging in big data with both statistical and machine learning methods under consideration. Preliminary results indicate that this is an opportune time to make these challenging but critical steps.