Methods for Forecasting Extreme Events with Machine Learning and Extreme Value Statistics

Extreme events such as infrastructures collapsing, environmental disasters, and financial crashes have catastrophic lasting consequences. The complex drivers of extreme events and their scarcity in historical records make foreseeing them statistically challenging. In particular, floods, heatwaves, wildfires, and hurricanes cause severe harm to humans and ecosystems, with seemingly unpredictable timing and magnitudes. Yet, with such devastating impacts, and with their increasing frequency and intensity under climate change, they are the most critical to predict accurately. Therefore, reliable forecasts and risk estimates are crucial for early warnings, disaster preparedness, and adaptation to save lives and reduce economic losses. They also help financial investors promptly mitigate losses, policymakers make informed decisions, and insurers be better prepared to sudden increases in claims. In that light, this thesis develops novel methodologies for accurately forecasting the conditional risk of extreme events and for understanding their drivers, by combining extreme value statistics with machine learning and causal inference. The first contribution introduces a method providing accurate extreme quantile predictions when the dependence on predictors is complex or dependent between observations, by combining the flexibility and versatility of neural networks with the extrapolation capabilities of extreme value statistics. The model can also forecast other risk metrics, such as high-threshold exceedance probabilities or expected shortfalls, as the entire conditional tail of the response variable is modelled. The second contribution provides an additional type of forecasts: prediction intervals. Our extreme conformal procedure predicts informative and adaptive high-confidence intervals of likely values for the response variable, when the required confidence level is too high for classical conformal methods to be applicable. The third contribution proposes a permutation test for causal discovery in extreme regimes, and a way to mitigate confounding effects, detrimental to the extremal causal analysis. The fourth studies the performance of state-of-the-art deep-learning global weather prediction models, during real extreme events, highlighting differences from operational physics-based systems. The new methods introduced in this thesis, and their implementation, aim to provide practical tools for risk assessment and forecasting, that are applicable to a wide range of domains.