CAREER: Structure Learning and Forecasting of Large-Scale Time Series

在现代生物科学和社会科学的许多领域，研究人员和从业人员试图利用大规模时间序列数据集来深入了解复杂系统的动态。例子包括使用时程基因表达数据集重建基因调控网络，使用神经生理信号对大脑网络架构进行功能连接分析，以及使用许多公司股票价格的历史数据监测金融市场的系统性风险。该项目的总体目标是开发可扩展的统计方法，用于使用高维时间序列（HDTS）数据集学习这种动态关系，并对其属性进行严格分析。这些方法在成功完成后，预计将有助于系统生物学中数据驱动的可检验假设生成，计算神经科学中基于成像的生物标志物搜索，并为金融风险管理和监测的监管政策提供信息。研究成果将被整合到一些教育和推广活动中，包括开发现代数据科学课程，并附带在线教科书，以及培训研究生和本科生。现有的HDTS数据集分析算法主要依赖于在机器学习中使用现代正则化，再加上为独立数据设计的平方误差损失。这与经典时间序列的核心建模理念形成鲜明对比，在经典时间序列中，观测值之间的时间依赖性被显式编码在似然或损失函数中，以提高结构学习和预测的准确性。该项目将通过设计新算法来缩小差距，其中时间依赖性和正则化使用依赖性感知机器学习方法相互通知。特别是，脉冲响应和分位数特定的图形模型在时域中，自适应正则化的图形模型在频域中，和随机森林，明确纳入时间依赖建立回归树，将被开发。这些方法将与领域专家协商，在来自基因组学、神经科学和金融经济学的真实的数据集上进行验证。研究结果将通过在统计、机器学习和其他科学期刊上发表同行评审的文章向公众传播。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

In many areas of modern biological and social sciences, researchers and practitioners seek to gain insight into the dynamics of a complex system using large-scale time series data sets. Examples include gene regulatory network reconstruction using time-course gene expression data sets, functional connectivity analysis of brain network architecture using neurophysiological signals, and monitoring systemic risk in the financial market using historical data on many firms' stock prices. The overarching goal of this project is to develop scalable statistical methods for learning such dynamic relationships using high-dimensional time series (HDTS) data sets, and provide a rigorous analysis of their properties. These methods, upon successful completion, are expected to aid data-driven testable hypothesis generation in systems biology, imaging-based biomarker search in computational neuroscience, and inform regulatory policy for financial risk management and monitoring.The research outcomes will be integrated into a number of education and outreach activities, including development of a modern data science curriculum with an accompanying online textbook as well as training of graduate and undergraduate students.Existing algorithms for analyzing HDTS data sets rely primarily on using modern regularization in machine learning coupled with a squared error loss designed for independent data. This is in sharp contrast with the core modeling philosophy of classical time series, where temporal dependence among observations is explicitly encoded in the likelihood or loss function to increase the accuracy of structure learning and prediction. This project will narrow the gap by designing new algorithms where temporal dependence and regularization inform each other using dependence-aware machine learning methods. In particular, impulse response and quantile-specific graphical models in the time domain, adaptively regularized graphical models in the frequency domain, and random forests that explicitly incorporate temporal dependence in building regression trees, will be developed. These methods will be validated on real data sets from genomics, neuroscience and financial economics in consultation with domain experts. Results will be disseminated to public by publishing peer-reviewed articles in statistics, machine learning and other scientific journals. Software implementations of algorithms developed in this project will be made publicly available in the form of R packages.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.