DMS-EPSRC: Change Point Detection and Localization in High-Dimensions: Theory and Methods

变化点分析是统计学中一个成熟的主题，它涉及到在时间序列中，更广泛地说，在随机和空间过程中，检测和定位数据生成分布中的突变。变化点分析是一个长期研究的课题，有着丰富的文献，它已经为实践者提供了大量完善的统计推断方法。这些技术被广泛应用于许多不同的应用中，以解决重要的现实生活问题，如安全监控、神经成像、金融交易、生态统计、气候变化、医疗状况监测、传感器网络、疾病爆发风险评估、流感趋势分析、遗传学等。然而，现有的变化点问题统计分析框架往往依赖于传统的参数化建模假设，这些假设不足以捕捉现代高维数据集的固有复杂性。本提案的总体目标是为脱机和顺序问题的高维和非参数设置的变化点分析开发新的理论和方法。

Change point analysis is a well-established topic in statistics that is concerned with detecting and localizing abrupt changes in the data generating distribution in time series and, more broadly, stochastic and spatial processes. A long-studied subject with a rich literature, change point analysis has produced a host of well-established methods for statistical inference available to practitioners. These techniques are widely used in many, diverse applications to address important real life problems, such as security monitoring, neuroimaging, financial trading, ecological statistics, climate change, medical condition monitoring, sensor networks, risk assessment for disease outbreak, flu trend analysis, genetics and many others. However, existing frameworks for statistical analysis of change point problems often rely on traditional modeling assumptions of parametric nature that are inadequate to capture the inherent complexity of modern, high-dimensional datasets. The broad goal of this proposal is to develop novel theories and methods for change point analysis in high-dimensional and nonparametric settings, for both offline and sequential problems.