Modeling Temporal Dynamics of Large Systems from High-Dimensional Time Series Data

要回答生物和社会科学中的许多问题，就需要了解一个大系统的组成部分如何动态地相互作用并产生紧急行为。例如，少数几家小但关系密切的公司同时倒闭可能会导致金融体系的巨大系统性损失。不同脑区神经生理信号之间的相互作用与人脑连接体的组织有关。这个项目的目的是开发严格和计算高效的统计方法，使用高维时间序列数据集联合建模这种大系统的时间动力学。这些方法将使研究人员能够更深入地了解这些系统的结构，并帮助制定更准确的数据驱动决策。预计正在开发的方法可用于临床神经科学，以寻找与神经系统疾病相关的功能连通性模式，以及用于金融监管，以监控系统风险和识别金融系统中具有系统重要性的公司。具体地说，本项目将专注于高维时间序列中的两类估计和推断问题：(I)发展估计高维谱密度和相干矩阵的新理论和方法，这可以被视为协方差和相关矩阵估计问题在高维时间序列中的自然推广；(Ii)发展新的理论机制来量化高维向量自回归模型中的不确定性(置信度和假设检验)。总的来说，这项研究将试图利用优化、统计学、信号处理和随机矩阵理论等学科的工具，弥合独立数据的高维统计和时间序列数据的当前前沿之间的差距。这种思想的智力统一可能会在以数据驱动的方式破译复杂系统的工作方式方面提供新的见解。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The answers to many questions in the biological and social sciences require understanding how the components of a large system dynamically interact with each other and give rise to emergent behavior. For instance, simultaneous failure of a handful of small but highly-connected firms can lead to huge systemic losses in the financial system. Interactions among neurophysiological signals in different brain regions relate to the organization of human brain connectome. This project aims to develop rigorous and computationally efficient statistical methods to jointly model the temporal dynamics of such large systems using high-dimensional time series datasets. These methods will enable researchers to gain deeper insights into the structure of these systems and help with more accurate data-driven decision making. It is anticipated that the methods under development can be used in clinical neuroscience to search for functional connectivity patterns associated with neurological disorders, and in financial regulation for monitoring systemic risk and identifying systemically important firms in the financial systems.Specifically, this project will focus on two classes of estimation and inference problems in high-dimensional time series: (i) developing novel theory and methods for estimating high-dimensional spectral density and coherence matrices, which can be viewed as a natural generalization of covariance and correlation matrix estimation problems to high-dimensional time series, and (ii) developing novel theoretical machinery to quantify uncertainty (confidence intervals and hypothesis tests) in high-dimensional vector autoregressive models. Broadly speaking, the research will attempt to bridge a gap between current frontiers of high-dimensional statistics for independent data and time series data using tools from disciplines including optimization, statistics, signal processing, and random matrix theory. This intellectual unification of ideas may provide novel insights in deciphering the workings of complex systems in a data-driven fashion.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.