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

协作研究：高维度的极端：因果关系、稀疏性、分类、聚类、学习

• 批准号: 2015242
• 负责人: Gennady Samorodnitsky
• 金额: $ 30万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2015242&HistoricalAwards=false
• 关键词: Collaborative; Research; Extremes; Dimensions; Causality

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situations, it has become clear that the preponderance of extremes events suggest that the steady-state assumption is no longer valid.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.

近年来，通过新闻报道和第一手经验，公众已敏锐地意识到极端事件，特别是极端天气状况，如持续的热浪、极端寒冷时期、龙卷风和飓风数量和强度的增加，或创纪录的降水量导致前所未有的洪水。 就在过去几年里，极端气候事件的保险索赔令人震惊，其中包括2019年4月的密苏里州洪水（108亿美元），2018年10月的飓风迈克尔（250亿美元），2017年12月的加州野火（187亿美元），2012年美国干旱/热浪（339亿美元）和2012年10月的飓风桑迪（734亿美元）。 这份清单不包括非气候极端事件，如2008年的金融危机和当前的新冠肺炎疫情。今天经历的许多与天气、环境、工业、流行病、经济或社交媒体有关的极端事件正在以更频繁的速度发生，这往往会在各种方面给我们的社会造成巨大损失，从金融到人类生活，再到我们的生活方式。虽然在稳态情况下对极端事件的发生有合理的理解，但很明显，极端事件的大量发生表明稳态假设不再有效。 这项研究的主要目标是试图了解各种因素的因果影响，这些因素来自一系列潜在的变量，包括不断变化的环境条件，美国境内的人口流动，不断变化的景观和不断变化的经济条件，对极端事件的频率和幅度。 从许多变量中，我们希望产生方法来提取数据中对描述和预测极端情况有直接影响的重要特征。 这项研究可能对需要预测和计划极端事件的政策制定者有用，从而制定明智的战略来减轻其对社会的影响。研究生的支持将用于跨学科的研究。这个研究项目的主要目标是设计新的工具，用于分析和建模极端的情况下，远远超出了经典极值理论的界限。这些包括检测通常是非线性的小得多的维度，可以提供足够的描述，在高维度的极端，我们希望应用强大的现代学习技术（如基于图的学习方法），使我们能够确定这个极端的支持数据。通常，检测描述高维极值的指数度量中的稀疏性，即，定位（通常是大量的）携带指数测度的大部分支持的低维区域将是本研究的关键焦点。本研究的第二个主要重点集中在小维度和大维度问题中的因果关系问题上。在最基本的形式中，如果X的某些变化（有时本身极端，但不总是如此）影响Y的尾部行为，则一组变量X被称为是依赖向量Y的尾部因果。这种类型的一个重要设置是极端事件因果关系的潜在结果框架，这将是该项目研究议程的主要焦点。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。