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: 2015379
• 负责人: Richard Davis
• 金额: $ 30万
• 依托单位: Columbia 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 2023-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2015379&HistoricalAwards=false
• 关键词: Collaborative; Research; Extremes; Dimensions; Causality; 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situations, it has become clear that the preponderance of extremes events suggest that the steady-state assumption is no longer valid.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，公众已经敏锐地意识到极端事件，特别是极端天气条件，例如延长的热浪，极度寒冷的时期，龙卷风和飓风的数量和强度的增加，或造成了创纪录的降水时期，导致了前所未有的洪水。 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). 该列表不包括非气候极端事件，例如2008年的金融危机和当前的Covid-19大流行。当今经历的许多极端事件都是天气，环境，工业，流行病学，经济或社交媒体相关的情况，它们的发生率更高，这通常以从财务到人类的生活再到我们的生活方式的各种方式给我们的社会带来巨大损失。尽管在稳态情况下，极端事件的发生率相当合理地理解，但很明显，极端事件的优势表明稳态假设不再有效。 这项研究的主要目的是试图从潜在的大量变量，包括不断变化的环境条件，美国境内的人口运动，改变景观以及不断变化的经济状况，对极端事件的频率和幅度的变化。 从许多变量中，我们希望产生方法，以提取数据直接影响和预测极端的数据中的重要特征。 这项研究可能是对需要预料并计划极端事件的政策制定者来使用的，从而导致明智的策略来减轻其对社会的影响。研究生的支持将用于跨学科研究。该研究项目的主要目标是设计新工具，用于分析和建模极端情况，这些工具远远超出了经典极端价值理论的界限。其中包括检测通常较小维度的非线性集，可以为高维度提供足够的极端描述，我们希望我们能够应用强大的现代学习技术（例如基于图的学​​习方法），从而使我们能够从数据中确定这种极端支持。通常，在指数量度中检测描述高维极端的稀疏性，即（通常是众多）低维区域的定位（通常是众多）对指数量度的支持，将是这项研究的重点。这项研究的第二个主要力量集中在大小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（有时是极端但并非总是如此），则认为一组变量X是因依赖矢量Y的尾巴因果关系。这种类型的尾声是极端事件的因果关系的潜在结果，这将是该项目的iNDERINAL INDER INTERCTION nsf derem teem teem teem teem teem nsf的主要重点，并且这将是一个重点。优点和更广泛的影响审查标准。