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: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=717097
• 关键词: 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.

实验设计是统计学中处理数据收集的一个分支，本文讨论了实验设计的三个研究方向。