BIGDATA:F: Statistical Learning with Large Dynamic Tensor Data

时间序列分析主要应用于发现观测数据随时间的相关和动态结构，以及准确预测这些数据在未来的潜在结果。在大数据时代，现代数据收集能力产生了大量的时间序列数据。 现在，在广泛的应用中会定期收集大型张量（或多维数组）数据。 例如，一组国家每季度报告一组经济指标，形成一个矩阵（二维数组）时间序列，每列代表一个国家，每行代表一个经济指标。一组国家不同类型商品的进出口量随时间的变化形成一个三维数组时间序列。该项目的目的是奠定基础并开发一个通用框架，以系统地研究此类张量系统的动力学，破译张量阵列中每个单独时间序列的联合行为，并提供准确预测的方法。该框架将包括一般和具体的统计模型、实际应用、统计方法及其理论和经验性质、计算算法和软件，以及在若干数据集中的实施。该研究可应用于从金融和经济学、环境科学、人类行为（例如社交网络）到神经科学和工程的应用领域。 该项目还涉及未来数据科学家的培训和教育。在大数据时代，大张量时间序列在广泛的应用中被常规地观察到。该项目旨在开发最先进的统计工具，以有效和高效地从如此庞大的复杂数据中提取有用的信息。这项工作涉及一个一般框架的统计学习与大型动态张量数据。 具体来说，该项目将开发一个通用类的张量因子模型，并针对特定应用进行修改，用于建模矩阵和张量值时间序列，动态网络和时空数据。研究结果有望直接应用于经济张量数据、进出口量时间序列、动态社交网络、污染监测、流体动力学问题和动态大脑连接网络。模型估计程序，沿着与他们的理论基础将被开发。这项研究将丰富统计学习的工具包，以解决一类非常重要和广泛遇到的大数据问题。该项目还涉及在统计学习及其应用领域对研究生和本科生进行研究培训。该项目将开发和传播免费软件，包括一系列用于研究的清洁数据集，以及一个永久维护的网站，作为未来动态张量研究的传播中心。将组织一次关于大型动态张量分析的国际会议。 计算算法的评估和大规模应用方法的实施将利用商业云服务提供商和NSF之间的协议提供的云计算资源，用于BIGDATA征集。

Time series analysis is mainly applied in the discovery of dependent and dynamic structure of observations over time, and in accurate prediction of potential outcomes of such data in the future. In the big-data era, modern data collection capabilities have led to massive amounts of time series data. Large tensor (or multi-dimensional array) data are now routinely collected in a wide range of applications. For example, a group of countries will report a set of economic indicators each quarter, forming a matrix (2-dimensional array) time series, with each column representing a country and each row representing an economic indicator. The import and export volume of different types of goods for a group of countries over time form a 3-dimensional array time series. The aim of the project is to lay a foundation and develop a general framework to systematically study the dynamics of such tensor systems, decipher the joint behavior of each individual time series in the tensor array, and provide methods for accurate prediction. The framework will include general and specific statistical models, practical applications, statistical methods and their theoretical and empirical properties, computational algorithms and software, and implementation in several data sets. The research can be applied to application areas ranging from finance and economics, environmental sciences, and human behavior (e.g. social networks) to neuroscience and engineering. The project also addresses the training and education of future data scientists. In the big-data era, large tensor time series are routinely observed in a wide range of applications. This project aims to develop state-of-the-art statistical tools to effectively and efficiently extract useful information from such big complex data. The work concerns a general framework of statistical learning with large dynamic tensor data. Specifically, the project will develop a general class of tensor factor models, with modifications for specific applications, for modeling matrix- and tensor-valued time series, dynamic networks, and spatial temporal data. The results are expected to be directly applicable to economic tensor data, import-export volume time series, dynamic social networks, pollution monitoring, problems in fluid dynamics, and dynamic brain connectivity networks. Model estimation procedures, along with their theoretical foundations will be developed. The research will enrich the toolkit of statistical learning for a highly important and widely encountered class of big-data problems. The project also involves research training of graduate and undergraduate students in the field of statistical learning and its applications. The project will develop and disseminate free software, including an array of cleaned data sets for research, and a permanently maintained website as a hub for dissemination of future dynamic tensor research. An international conference on large dynamic tensor analysis will be organized. Evaluation of the computational algorithms and implementation of the methods for large scale applications will leverage cloud computing resources provided through an agreement between commercial cloud service providers and NSF for the BIGDATA solicitation.