Parsimonious high-dimensional and matrix-variate copula modeling

简约高维矩阵变量联结建模

• 批准号: RGPIN-2022-03867
• 负责人: Murphy, Orla
• 金额: $ 1.38万
• 依托单位: Dalhousie 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=759070
• 关键词: Parsimonious; dimensional; matrix; variate; copula

With technology yielding larger and more diverse data collections, many scientific domains seek innovative ways to investigate "big data". Although statistical methods are the standard scientific procedure for analyzing and interpreting data, many of the standard approaches cannot be used to analyze big data. This inability can be due to large computational burdens, or in some cases, the standard methods cannot be extended to handle large numbers of variables. This proposed research will develop novel methods for the assignment of observations in big data to groups based on commonalities, without any prior knowledge of the correct grouping. This procedure is called clustering and is a type of unsupervised learning method as it does not assume prior knowledge of the correct assignments or even the number of groups. Clustering is used to identify underlying structures and patterns in the data and may be used to localize analyses into groups. This research will focus on developing innovative clustering methods to analyze data with many recorded variables that have socio-economic and environmental importance (e.g., gene expression, economic, health, and geo-referenced spatial data) as well as three-way data (e.g., gray-scale images and multiple variables recorded over time aka "longitudinal data"). This work will advance our understanding in the use of clustering to model big data. Methods developed will be presented in freely available statistical software packages in R for use by practitioners and researchers. This research will impact the analysis of big data in diverse fields including medicine, economics, marketing, food science, biology, and environmental sciences.

随着技术产生更大、更多样化的数据收集，许多科学领域都在寻求创新的方法来研究“大数据”。尽管统计方法是分析和解释数据的标准科学程序，但许多标准方法不能用于分析大数据。这种无能为力的原因可能是计算负担太大，或者在某些情况下，标准方法无法扩展以处理大量变量。这项拟议的研究将开发新的方法，将大数据中的观测数据分配给基于共性的组，而不需要事先知道正确的分组。这个过程被称为聚类，是一种无监督的学习方法，因为它不假设正确分配的先验知识，甚至不需要了解组的数量。聚类用于识别数据中的底层结构和模式，并可用于将分析本地化为组。这项研究将侧重于开发创新的聚类方法，以分析具有社会经济和环境重要性的许多记录变量的数据(例如，基因表达、经济、健康和地理参考空间数据)以及三向数据(例如，随着时间的推移记录的灰度级图像和多个变量，即“纵向数据”)。这项工作将增进我们对使用集群为大数据建模的理解。所开发的方法将在R中免费提供统计软件包，供从业人员和研究人员使用。这项研究将影响医学、经济学、营销学、食品科学、生物学和环境科学等多个领域的大数据分析。