Collaborative Research: Change Point Testing and Estimation with Irregular Signals

The project aims to advance the field of statistical change-point detection by developing novel methods and their associated theory to handle complex data with irregular signals. Unlike the traditional setting in which signals before and after the change point are often assumed to differ by a constant shift, irregular signals refer to the situation when the post-change signal may vary in highly unpredictable ways without any pre-specifiable pattern or structure. This can pose a tremendous challenge on many existing change-point tests, often resulting in notable reductions in their statistical power and increasing their vulnerability to maliciously designed adversarial attacks. By allowing the post-change signals to be irregular and not necessarily follow the standard assumptions as in conventional change-point analyses, the research developed in this project is expected to lead to more robust and next-generation statistical and machine learning protocols and toolboxes with rigorous theoretical guarantees for change-point detection in a wide range of applications. For example, detecting abrupt changes in power grids, attacks in sensor networks, or emerging trends in social networks all require powerful methods for detecting irregular changes. As a result, the research will advance not only the field of statistics but also a range of other disciplines including machine learning and artificial intelligence where data with irregular signals may arise. The research will also be integrated into the undergraduate and graduate education at participated institutions to equip students with advanced yet accessible statistical and machine learning knowledge for analyzing data with irregular signals. The research involves the development of novel statistical methods and their associated theory for change-point detection and estimation in the presence of potentially irregular signals. To quantity the uncertainty in the estimated signals from dependent and noisy data, a causal representation framework is employed with a suitably constructed functional dependence measure to quantify the effect of dependence via the technique of perturbation and innovation coupling. This enables the use of deep probabilistic tools, such as the invariance principle and Gaussian approximation results, for a general class of dependent processes to guide the selection of a statistically appropriate alarm threshold for detecting change points in the presence of irregular signals. The project aims to address change-point detection under irregular signals both in the offline setting, where the analysis is performed after all the data are collected, and in the online setting, where sequential testing becomes desirable as data arrive. In addition, different asymptotic schemes are considered to address situations in which stable historical data are available and when such data are not available to practitioners. The research is also expected to promote scientific and technological advances in applications that require rapid anomaly detection with complex alternatives. 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. NSF Award ID: 2610300 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Ting Zhang | Institution: University of Georgia Research Foundation Inc, ATHENS, GA | Award Amount: $150,000 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2610300 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2610300.html