Collaborative Research: Extremes in High Dimensions: Causality, Sparsity, Classification, Clustering, Learning

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In recent years, through news reports and first-hand experience, the general public has become keenly aware of extreme events, in particular, of extreme weather conditions such as extended heat waves, periods of extreme cold, an increase in the number and intensity of tornadoes and hurricanes, or periods of record precipitation resulting in unprecedented floods. Just in the past few years, the insurance claims from extreme climatic events have been staggering, which include the Missouri River flood in April 2019 ($10.8B), Hurricane Michael in October 2018 ($25B), the California wildfires in December 2017 ($18.7B), the US drought/heatwave in 2012 ($33.9B), and Hurricane Sandy in October 2012 ($73.4B). This list does not include non-climatic extreme events such as the financial crisis from 2008 nor the current covid-19 pandemic. Many of the extreme events experienced today that are weather, environmental, industrial, epidemiological, economic, or social media related are occurring at a more frequent rate, which often result in huge losses to our society in a variety of ways from financial to human life to our way of life. While the occurrence of extreme events is reasonably well understood in steady state situations, it has become clear that the preponderance of extremes events suggest that the steady-state assumption is no longer valid. The key objective of this research is to try to understand causal impacts of various factors from a potentially large array of variables including changing environmental conditions, demographic movements within the US, changing landscapes, and changing economic conditions, on the frequency and magnitude of extreme events. From many variables, we hope to produce methodology to extract the important features in the data that have a direct impact on describing and predicting extremes. This research is potentially of use to policymakers who need to anticipate and plan for extreme events leading to sensible strategies for mitigating their impact on society. The graduate student support will be used for interdisciplinary research.The principal goal of this research project is to design new tools for analyzing and modeling extremes in a myriad of situations that go well beyond the boundaries of classical extreme value theory. These include detection of often nonlinear sets of much smaller dimension that can provide an adequate description of extremes in high dimensions, for which we hope to apply the powerful modern learning techniques (such as graph-based learning methods) that allow us to determine this extremal support from the data. In general, detecting sparsity in the exponent measure describing high-dimensional extremes, i.e., locating (often numerous) low-dimensional regions which carry most of the support of exponent measure will be a key focus of this research. A second main thrust of this research centers on the issue of causality in both small and large dimensional problems. In the most basic form, a set of variables X is said to be tail causal to a dependent vector Y if certain changes in X (sometimes themselves extreme but not always so) impact the tail behavior of Y. An important setting of this type is the potential outcomes framework for causality of extreme events, which will be a major focus in this project's research agenda.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.