Baseline designs, space-filling designs and big data research

基线设计、空间填充设计和大数据研究

• 批准号: RGPIN-2020-04548
• 负责人: Tang, Boxin
• 金额: $ 3.13万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=765792
• 关键词: Baseline; designs; space; filling; big; Baseline; designs; space; filling; big

This proposal discusses three research directions in experimental design, a branch of statistics that deals with data collection. The first direction is on baseline designs. Factorial designs are commonly employed in science and technology to study how a response variable depends on a number of potential factors. Analysis is generally done using orthogonal effects, which is called the orthogonal parametrization. When factors have a default setting,  a baseline parametrization of effects becomes more appropriate. Nonorthogonality of baseline effects raises serious challenges, and only very limited results are available to this date. The proposal will examine a new approach by establishing and utilizing a relationship between the two types of parametrization. Rich results are expected from this novel approach. The next direction is on space-filling designs. Nowadays, scientific and technological investigations are routinely conducted on computers. For complex computer models, it is prudent to build a surrogate model for fast updating and predictions. The statistical approach to this problem is via computer experiments, where researchers build surrogate models based on a set of inputs and corresponding outputs. Judicious selection of inputs is crucial. Space-filling designs are most suited for computer experiments. The most attractive approach is to use strong orthogonal arrays because of their guaranteed space-filling properties. Despite recent advances, some major problems remain open and they are topics for the proposed research. One example is to find strong orthogonal arrays that also perform well under other criteria such as those of orthogonality, distance or discrepancy.  The third direction is about big data research. We consider a measurement constrained supervised learning problem. A big data set is available that contains observations on explanatory variables, but information on a response variable is very expensive to obtain. This situation necessitates the selection of a sample of the big data set; one can then collect information on the response variable for this small data set. Two popular methods are a sampling method using leverages and a deterministic method, called IBOSS, using design theory. While the IBOSS enjoys appealing properties compared to the sampling method, it heavily relies on a pre-specified linear model. The proposed research examines the use of space-filling designs for subdata selection. This approach is robust to model misspecification, and expected to perform well under various models. Training HQP is integral part of the proposed research. Each of the three research directions outlined above has enough topics to train at least one PhD student. The proposed research also contains a plentiful supply of research topics for training undergraduate and MSc students. Details on how to integrate HQP training into the proposed research will be provided in the HQP training plan.

该建议讨论了实验设计中的三个研究方向，这是涉及数据收集的统计分支。第一个方向是基线设计。阶乘设计通常在科学技术中使用，以研究响应变量如何取决于许多潜在因素。通常使用正交效应进行分析，这称为正交参数。当因素具有默认设置时，效果的基线参数变得更加适当。基线效应的非正交性提出了严重的挑战，到目前为止，结果只有非常有限的结果。该提案将通过建立和利用两种类型的参数之间的关系来检查一种新方法。这种新颖的方法可以预期丰富的结果。下一个方向是在空间填充设计上。如今，科学和技术调查通常是在计算机上进行的。对于复杂的计算机模型，构建用于快速更新和预测的替代模型是谨慎的。解决此问题的统计方法是通过计算机实验，研究人员基于一组输入和相应的输出来构建替代模型。明智的投入选择至关重要。空间填充设计最适合计算机实验。最有吸引力的方法是使用强大的正交阵列，因为它们具有保证的空间填充特性。尽管最近进步，但一些主要问题仍然开放，它们是拟议研究的主题。一个例子是找到在其他标准（例如正交性，距离或差异的标准）下表现良好的强差阵列。第三个方向是关于大数据研究。我们考虑了一个受限制的监督学习问题的测量。有一个大数据集，其中包含对爆炸变量的观察，但是有关响应变量的信息非常昂贵。这种情况需要选择大数据集的样本；然后，可以为此小数据集收集有关响应变量的信息。两种流行的方法是使用杠杆的采样方法，使用设计理论的确定性方法称为Iboss。与采样方法相比，IBOSS具有外观特性，但它在很大程度上依赖于预先指定的线性模型。拟议的研究考试将填充空间设计用于子数据选择。这种方法可用于模型错误，并有望在各种模型下表现良好。培训HQP是拟议研究的组成部分。上面概述的三个研究指示中的每一个都有足够的主题来培训至少一名博士生。拟议的研究还包含了培训本科生和MSC学生的大量研究主题。 HQP培训计划将提供有关如何将HQP培训整合到拟议研究中的详细信息。