Big Data Modeling via Moment-Based Methodologies and the Statistical Analysis of Spatio-Temporal Measurements

通过基于矩的方法进行大数据建模以及时空测量的统计分析

• 批准号: RGPIN-2019-06323
• 负责人: Provost, Serge
• 金额: $ 1.17万
• 依托单位: University of Western Ontario
• 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=715354
• 关键词: Big; Data; Modeling; via; Moment

Nowadays, multivariate data originating for instance from biostatistics, meteorological, engineering or astronomical studies are becoming more challenging to data mine in light of their increasing complexity and size. Efficient methodologies that are principally based on joint sample moments and are independent of the sample size are advocated in this research proposal as they are ideally suited for analyzing Big Data'. As well, such techniques mitigate the curse of dimensionality. The distributional representations resulting from generalizations of widely utilized models are expressed in functional forms that allow for interpretability, lend themselves to algebraic manipulations and give rise to highly flexible copulae, which describe the dependence between variables of interest. Being remarkably versatile, such models should find applications in reliability theory and quality assurance testing. The results will be adapted to the context of regression with a view to discarding uninformative variables and eliciting relevant patterns and relationships between the significant ones. As well, both novel and established multivariate methodologies such as hierarchical clustering analysis and data visualization techniques such as scatterplot matrices will be brought to bear to great advantage in the fields of neuroimaging - for assessing the dissimilarities between vectors of responses associated with certain stimuli - and environmetrics - for detecting trends in the face of climatic changes. As well, they should enhance the understanding of the underlying processes and, for instance, lead to advances in predictive analytics in connection with the occurrence of catastrophic events such as floods and earthquakes. The software documentation and source code to be developed for implementing the planned distributional breakthroughs shall be made available. Various approaches will be devised to extract pertinent distributional information from relatively small subsets of large-scale data sets. Once utilized in conjunction with innovative data reduction and variable selection techniques, the modeling methodologies being herein advocated will permit to process more rapidly massive spatio-temporal and higher-dimensional data sets that frequently arrive in streams as in the cases of high throughput cancer screening and DNA sequencing, the burgeoning blockchain technologies, metadata analyses, and the fast expanding field of artificial intelligence, which is at the core of autonomous and interactive systems such as self-driving vehicles. By addressing both volume and velocity in connection with the analysis of massive and complex streaming data, the proposed generalized models and innovative moment-based methodologies herald a paradigmatic shift in the processing of large-scale multivariate observations.

如今，来自生物统计学、气象、工程或天文学研究的多元数据由于其复杂性和规模的增加，对数据挖掘变得越来越具有挑战性。本研究建议提倡主要基于联合样本矩且独立于样本量的高效方法，因为它们非常适合分析大数据。同样，这些技术减轻了维度的诅咒。由广泛使用的模型的一般化产生的分布表示以函数形式表示，允许可解释性，使其适合代数操作，并产生高度灵活的联结，它描述了感兴趣的变量之间的依赖关系。这些模型非常通用，应该在可靠性理论和质量保证测试中得到应用。