Sparse and efficient methods for extreme events
Seminar in Mathematics
Abstract: Natural hazards such as heat waves or flooding are driven by very few rare events and may cause large costs in addition to their severe impacts on human health. The changing climate seems to alter the occurrence of such extreme scenarios even more strongly than the average values and an increasing number of record-shattering events occur around the world. We present recent developments on how the risk of such extreme scenarios can be assessed more accurately in modern applications with high-dimensional and complex data. The first class of methods is concerned with the out-of-sample prediction problem in machine learning, where either the response or the predictors in the test data go beyond the range of the training data. The second class of methods relies on the notion of extremal graphical models introduced in Engelke and Hitz (2020, JRSSB). They enable the analysis of complex rare events on network structures (e.g., floods) or large-scale spatial data (e.g., heat waves). We discuss data-driven structure learning algorithms that estimate graphs through L_1 penalization in possibly high dimensions. Recent results show that the underlying notion of extremal conditional independence arises as a special case of a much more general theory for limits of sums and maxima of independent random vectors.
Abstract: Natural hazards such as heat waves or flooding are driven by very few rare events and may cause large costs in addition to their severe impacts on human health. The changing climate seems to alter the occurrence of such extreme scenarios even more strongly than the average values and an increasing number of record-shattering events occur around the world. We present recent developments on how the risk of such extreme scenarios can be assessed more accurately in modern applications with high-dimensional and complex data. The first class of methods is concerned with the out-of-sample prediction problem in machine learning, where either the response or the predictors in the test data go beyond the range of the training data. The second class of methods relies on the notion of extremal graphical models introduced in Engelke and Hitz (2020, JRSSB). They enable the analysis of complex rare events on network structures (e.g., floods) or large-scale spatial data (e.g., heat waves). We discuss data-driven structure learning algorithms that estimate graphs through L_1 penalization in possibly high dimensions. Recent results show that the underlying notion of extremal conditional independence arises as a special case of a much more general theory for limits of sums and maxima of independent random vectors.
Practical information
- Informed public
- Free
- This event is internal
Organizer
- Institute of Mathematics
Contact
- Prof. Maryna Viazovska, Director