Efficient Algorithms with Statistical Guarantees for High Dimensional Time Series

各种工业和科学领域都在产生高维时间序列数据。宏观经济指标、股市表现和工业互联网传感器产生的时间序列对经济具有巨大价值。在系统生物学和神经科学中产生的时间序列可以使我们更好地了解人类健康和疾病。经典的统计方法处理高维时间序列的能力有限。因此，开发用于分析高维时间序列的统计工具是社会迫切关注的问题。该项目发展了理论和可扩展算法，以提高我们从高维时间序列数据中分析和提取有意义信息的能力。本项目将在高维统计、大规模优化和时间序列分析三个领域的界面上拓展研究前沿。将追求三个相互关联的研究目标。首先，将建立理论工具来分析高维时间序列线性预测方法在对时间序列生成过程的温和假设下的性能。其次，将为计算高维向量自回归（VAR）模型的最大似然估计量的高效交替最小化替代方案提供统计保证。第三，将开发用于在高维时间序列观测连续到达的情况下估计和预测的快速在线算法。

Various industrial and scientific fields are generating high-dimensional time series data. Time series generated by macroeconomic indicators, stock market performance, and sensors in the industrial internet are of huge value to the economy. Time series generated in systems biology and neuroscience can lead to a better understanding of human health and diseases. Classical statistical methods are limited in their ability to deal with high-dimensional time series. Developing statistical tools for the analysis of high-dimensional time series is thus of pressing concern to society. This project develops both theory as well as scalable algorithms for advancing our ability to analyze and extract meaningful information from high-dimensional time series data.This project will expand the frontier of research at the interface between three areas: high-dimensional statistics, large-scale optimization, and time series analysis. Three interrelated research aims will be pursued. First, theoretical tools to analyze the performance of linear prediction methods for high-dimensional time series under mild assumptions about the generative process underlying the time series will be built. Second, statistical guarantees for computationally efficient alternating minimization based alternatives to computing the maximum likelihood estimator for high-dimensional vector autoregressive (VAR) models will be provided. Third, fast online algorithms for estimation and forecasting in a setting where the high-dimensional time series observations arrive sequentially will be developed.