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

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有效方法，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。结果将适用于回归的情况，以期抛弃没有资料的变量，并得出有关的模式和重要变量之间的关系。同样，新的和已建立的多变量方法，如分层聚类分析和数据可视化技术，如散点图矩阵，将在神经成像领域发挥巨大的优势——用于评估与某些刺激相关的反应向量之间的差异——以及环境计量学——用于检测气候变化的趋势。同时，它们应该加强对潜在过程的理解，例如，在与洪水和地震等灾难性事件的发生有关的预测分析方面取得进展。应当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。一旦与创新的数据简化和变量选择技术结合使用，本文所提倡的建模方法将允许更快地处理大量的时空和高维数据集，这些数据集经常出现在流中，例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互动系统的核心。通过处理与大量和复杂流数据分析相关的体积和速度，所提出的广义模型和创新的基于矩的方法预示着大规模多变量观测处理的范式转变。

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.