Efficient Algorithms with Statistical Guarantees for High Dimensional Time Series

高维时间序列具有统计保证的高效算法

• 批准号: 1612549
• 负责人: Ambuj Tewari
• 金额: $ 12万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-01 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1612549&HistoricalAwards=false
• 关键词: Efficient; Algorithms; Statistical; Guarantees; Dimensional

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.

各种工业和科学领域正在产生高维时间序列数据。由宏观经济指标、股市表现和工业互联网中的传感器生成的时间序列对经济具有巨大价值。系统生物学和神经科学中产生的时间序列可以更好地了解人类健康和疾病。传统的统计方法在处理高维时间序列时能力有限。因此，开发用于高维时间序列分析的统计工具是社会迫切关注的问题。该项目开发理论和可扩展算法，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。该项目将扩展三个领域之间接口的研究前沿：高维统计、大规模优化和时间序列分析。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的线性预测方法的性能，对时间序列的生成过程进行温和的假设。第二，将提供用于计算高维向量自回归（VAR）模型的最大似然估计的基于交替最小化的替代方案的计算效率的统计保证。 第三，快速在线算法的估计和预测的设置中，高维时间序列观测顺序到达将被开发。