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: 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=765669
• 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，源自生物统计学，气象，工程或天文学研究的多元数据源于数据矿山的越来越挑战，鉴于它们的复杂性日益增加和规模。在本研究建议中提倡主要基于联合样本矩并独立于样本量的有效方法，因为它们非常适合分析“大数据”。同样，这种技术减轻了维度的诅咒。广泛使用模型的概括所产生的分布表示以功能形式表达，可以解释性，使其自身进行代数操作并产生高度灵活的Copulae，以描述感兴趣的变量之间的依赖性。这种模型非常通用，应该在可靠性理论和质量保证测试中找到应用。结果将适用于回归的上下文，以丢弃非信息变量，并引起相关模式和重要的模式。 As well, both novels and established multivariate methods 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 environmental metrics - for detecting trends in the face of crymatic changes.同样，它们也应增强对基本过程的理解，例如，与灾难性事件（如地板和地震）有关的预测分析的进步。应提供用于实施计划的分销突破的软件文档和源代码。将设计各种方法来从相对较小的大规模数据集的子集中提取相关的分布信息。 Once utilized in conjunction with innovative data reduction and variable selection techniques, the modeling methods being herein advocated will permit to process more rapidly massive spatial-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自动驾驶汽车等自主和互动系统的核心。通过与大规模和复杂流数据分析有关的体积和速度，提出的广义模型和基于创新的力矩方法预示了大规模多变量观察的处理范式转移。