Project

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Graph structures, sparsity and high-dimensional inference for extremes

Applicant Engelke Sebastian
Number 186858
Funding scheme Eccellenza grant
Research institution Research Center for Statistics Geneva School of Economics and Management Université de Genève
Institution of higher education University of Geneva - GE
Main discipline Mathematics
Start/End 01.09.2020 - 31.08.2025
Approved amount 1'492'033.00
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Keywords (7)

extreme value theory; structure learning; high dimensions; asymptotic independence; graphical models; causal inference; dependence modeling

Lay Summary (German)

Lead
Hitzewellen, Überschwemmungen und andere Naturkatastrophen werden durch sehr seltene Extremereignisse ausgelöst, welche gravierende Kosten für unsere Wirtschaft, Umwelt und Gesundheit mit sich bringen. In Zeiten des Klimawandels wird es immer wichtiger, die Eintrittswahrscheinlichkeiten solcher Ereignisse akkurat abzuschätzen, um geeignete Schutzmaßnahmen treffen zu können. Die Extremwerttheorie beschäftigt sich mit der Quantifizierung solcher Risiken. Da typischerweise in der Vergangenheit nur wenige extreme Beobachtung vorhanden sind, ist die Entwicklung effektiver statistischer Modelle herausfordernd und aktuell ein aktives Forschungsgebiet.
Lay summary
Während in den letzten Jahrzehnten große Fortschritte in der Analyse von univariaten Extremereignissen gemacht wurde, ist das Ziel dieses Projektes die Entwicklung einer neuen mathematischen Theorie für die Analyse sogenannter multivariater Extremwertereignisse, also Ereignisse, bei denen mehrere Variablen ungewöhnlich hohe Werte annehmen. Dies können beispielsweise starke Regenfälle an mehreren Orten gleichzeitig sein, oder hohe Verluste mehrerer Baken am gleichen Tag, die ein systematisches Risiko für die gesamte Finanzwirtschaft darstellen. Im Detail beschäftigt sich dieses Projekt mit (i) dem Lernen von grafischen Strukturen in Extremereignissen, welches neue Erkenntnisse über Verbindungen und Risikoausbreitung in komplexen Systemen ermöglicht. Außerdem wird untersucht, wie (ii) statistisch ein kausaler Zusammenhang zwischen extremen Ereignissen nachgewiesen werden kann. Ein weiteres Ziel ist es, (iii) komplexe extreme Szenarien zu modellieren und somit eine Möglichkeit zu haben, mit Simulationen das künftige Risiko auswerten zu können.
Direct link to Lay Summary Last update: 19.06.2020

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Abstract

Natural hazards such as heat waves, heavy rainfall or flooding are driven by very few rare events and may have large economic and ecological costs in addition to their potential for severe impacts on human health. The accurate statistical assessment of the small probabilities of occurrence of such extreme scenarios is thus crucial in many different settings. The area of research concerned with the quantification of the risk of these rare events, known as extreme value theory, is a rapidly evolving field with influences from probability theory, statistics and applied science. The analysis of univariate tail distributions, such as the value at risk of a financial asset or the computation of a 100-year flood event in a specific city, is well studied in the literature. Recent advances in theory and practice concentrate on the dependence between rare events in complex multivariate or spatial systems. The motivation for these extensions comes from a variety of different applications, in fields such as hydrology, meteorology, finance and actuarial science. Climate scientists observe an increasing risk of compound events due to a combination of different variables, such as wildfires caused by low precipitation and extreme heat. Similarly, the systemic risk of a financial system depends highly upon the connections among core institutions.Natural hazards such as heat waves, heavy rainfall or flooding are driven by very few rare events and may have large economic and ecological costs in addition to their potential for severe impacts on human health. The accurate statistical assessment of the small probabilities of occurrence of such extreme scenarios is thus crucial in many different settings. The area of research concerned with the quantification of the risk of these rare events, known as extreme value theory, is a rapidly evolving field with influences from probability theory, statistics and applied science. The analysis of univariate tail distributions, such as the value at risk of a financial asset or the computation of a 100-year flood event in a specific city, is well studied in the literature. Recent advances in theory and practice concentrate on the dependence between rare events in complex multivariate or spatial systems. The motivation for these extensions comes from a variety of different applications, in fields such as hydrology, meteorology, finance and actuarial science. Climate scientists observe an increasing risk of compound events due to a combination of different variables, such as wildfires caused by low precipitation and extreme heat. Similarly, the systemic risk of a financial system depends highly upon the connections among core institutions.Even though research in this area is very active, there is still little understanding of the probabilistic structures of the underlying models. This limits statistical modeling of rare events to fairly moderate dimensions so far, while data sets in risk applications become more complex and higher dimensional. Conditional independence, graphical models and sparsity are key concepts for parsimonious models in high dimensions and for learning structural relationships in the data. For multivariate extremes, these notions have only recently been properly defined and there is still much potential to explore their tight links to high-dimensional statistics, causal inference and machine learning. The main objective of this project is to follow this path and to develop novel mathematical theory and powerful statistical tools for modern applications of extremes. The first part of the planned research agenda tackles the problem of learning extremal graphical structures underlying the data. A version of the highly popular graphical lasso estimator will be developed to perform automatic model selection in extremes through regularization. This opens the door to high-dimensional settings where the number of model parameters is comparable to or even larger than the number of samples. In the second part, directed graphical models and Bayesian networks will be introduced for extreme value distributions. These notions form the basis for causal inference for rare events and have many possible applications, such as the attribution of extreme weather associated with climate change. In real data, the classical assumptions of multivariate extremes are often violated since the dependence becomes weaker for more severe scenarios. Flexible models for this case, called asymptotic independence, are urgently required and will be studied in the third part of this project. Two workshops on graphical models and high-dimensional extremes will be organized within the scope of this Eccellenza grant.
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