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，源自例如生物统计学、气象学、工程学或天文学研究的多变量数据由于其日益增加的复杂性和规模而变得对数据挖掘更具挑战性。有效的方法，主要是基于联合样本矩和独立的样本大小，提倡在这个研究建议，因为它们非常适合分析大数据。同样，这些技术减轻了维度灾难。分布表示广泛使用的模型的概括所产生的功能的形式，允许解释性，借给自己的代数操作，并产生高度灵活的copulae，它描述了相关变量之间的依赖关系。作为显着的通用性，这样的模型应该在可靠性理论和质量保证测试中找到应用。 结果将根据回归的情况加以调整，以排除无意义的变量，并得出相关的模式和重要变量之间的关系。此外，新的和建立的多变量方法，如层次聚类分析和数据可视化技术，如散点图矩阵，将带来承担在神经成像领域的巨大优势-用于评估与某些刺激相关的响应向量之间的差异-和气候变化指标-用于检测在面对气候变化的趋势。此外，它们还应该加强对潜在过程的理解，例如，导致与洪水和地震等灾难性事件发生有关的预测分析的进步。应提供为实现计划的分布式突破而开发的软件文档和源代码。 将设计各种方法，从大规模数据集的相对较小的子集中提取相关的分布信息。一旦与创新的数据缩减和变量选择技术结合使用，本文所倡导的建模方法将允许更快速地处理大量时空和高维数据集，这些数据集经常以流的形式到达，如高通量癌症筛查和DNA测序、新兴的区块链技术、元数据分析和快速扩展的人工智能领域。这是自动驾驶汽车等自主和交互系统的核心。 通过解决大量和复杂的流数据的分析，所提出的广义模型和创新的基于矩的方法，预示着在处理大规模的多变量观测的范式转变。