Title: Learning Extremal Dependence Structures Through Artificial Intelligence

Duration: 01.10.2023 – 31.12.2024

Research Area: Artificial intelligence, extreme value theory

Analyzing the dependence between extreme events is crucial for various domains. For example, one may wish to quantify the dependence between extreme weather events at different spatial locations or understand how one stock crashing affects the probability of other stocks also following suit. Due to the recent emergence of this field, conventional approaches for modeling extremal dependence struggle with high dimensions and often necessitate specifying rigid, parametric models, limiting their practical applicability.

In this project, we propose leveraging neural networks to model extremal dependence. Our approach can be applied in higher dimensions than existing approaches and eliminates the need for predefined model forms, providing a useful and practical tool for assessing dependence between extreme events.

Aims

In this project, we have four major aims:

1. To extend the study of extremal depedence to higher dimensional settings.
2. To remove the need for specifying rigid, parametric forms when estimating extremal dependence structures in practice.
3. To evaluate the performance of neural networks for capturing extremal dependence.
4. To design an optimal neural network architecture for extremal dependence modelling.

Problem

Existing approaches for modeling extremal dependence are typically limited to low (2 or 3) dimensional settings. Moreover, many of these approaches make strong prior assumptions about the form of dependence. In this setting, model mis-specification can result in large over- or under-estimation, rendering inference from such approaches less reliable. Furthermore, the use of artificial intelligence for extremal dependence modeling has yet to be explored, motivating the development of novel approaches in this area.

Practical example

We have tested our methodology using metocean datasets, where quantifying the dependence between extremes of multiple variables (wave height, wind speed, wind direction, wave period, precipitation, etc.) is crucial for the design of ocean structures, such as wind turbines. We also intend to use our framework for modeling extremes between river flow observations at multiple locations. Both applications will allow for a more accurate and robust risk assessment in practice, enabling stakeholders to make more informed decisions.

Technology

• Neural network modelling via Keras in the R computing language.
• Application of the geometric multivariate extremes framework.
• Quantile regression techniques.

Outlook

The project aims to provide a deeper understanding of extremal dependence structures in practical settings. Neural networks, with their capacity for complex pattern recognition, offer a promising avenue for uncovering intricate relationships in observed extreme events. We hope the methodology we develop can be used in practice to help with decision-making when considering risks related to extreme events.

Team

Lead

• Prof. Dr. Anita Behme

Team Members

• Dr. Callum Murphy-Barltrop

Partners

• Dr. Reetam Majumder (North Carolina State University)
• Dr. Jordan Richards (University of Edinburgh).