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

如今，来自生物统计学、气象学、工程学或天文学研究的多变量数据随着其复杂性和规模的增加而对数据挖掘提出了更大的挑战。在本研究方案中，提倡主要基于联合样本矩并且与样本量无关的高效方法，因为它们非常适合于分析大数据。同样，这些技术也缓解了维度的诅咒。由广泛使用的模型的推广产生的分布表示以函数形式表示，该函数形式允许可解释性，适合于代数操作，并产生高度灵活的联结，其描述感兴趣的变量之间的相关性。由于这种模型具有显著的通用性，应该会在可靠性理论和质量保证测试中得到应用。 结果将根据回归的情况加以调整，以期摒弃不具信息性的变量，并引出相关模式和重要变量之间的关系。此外，新的和已建立的多变量方法，如等级聚类分析和数据可视化技术，如散点图矩阵，都将在神经成像领域发挥巨大优势--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--用于检测面对气候变化的趋势。此外，它们还应加强对潜在过程的了解，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。应提供为实施计划中的分配突破而开发的软件文档和源代码。 将设计各种方法来从大型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，本文所倡导的建模方法将允许更快速地处理频繁到达流中的海量时空和高维数据集，如高通量癌症筛查和DNA测序、新兴的区块链技术、元数据分析以及快速扩展的人工智能领域，人工智能领域是自动驾驶车辆等自动和交互系统的核心。 通过在分析海量和复杂的流数据时同时处理体积和速度，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例转变。

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.