Extreme Statistics: Modern Solutions and Open Challenges in the Modeling and Inference of Complex High-Impact Events
Seminar in Mathematics
Abstract: Rare, low-probability events often lead to the biggest impacts. Therefore, the development of cutting-edge statistical machine learning approaches for modeling, predicting and quantifying risks is of utmost importance in a variety of fields of applications. Climate scientists, insurers, engineers, and financial analysts have indeed realized that the greatest risks are often caused by changes in the intensity, frequency, extent, and persistence of extreme events, rather than changes in their average behavior. However, while datasets are often massive in modern-day applications, extreme events are always scarce by nature. This makes it doubly challenging: models needed to realistically describe the dependence structure of high-dimensional random vectors are becoming increasingly complex, but the number of independent replicates used to fit these models remains relatively small. It is thus very important to design specialized models with strong theoretical support for reliable extrapolation to yet-unseen risk levels, as well as efficient inference methods to fit them to big datasets. In this colloquium, I will first provide a quick overview of classical models for spatial extremes and their severe methodological and computational limitations. I will then describe recent progress we have made to develop novel sub-asymptotic spatial models with an improved flexibility in their tail structure. To overcome computational challenges when performing inference, I will then discuss neural Bayes estimators, which are general, amortized, likelihood-free estimators constructed from permutation-invariant neural networks, that we recently developed for near-optimal and fast inference in complex models. Post-training, these estimators allow estimation of model parameters and uncertainty quantification in just a fraction of second. I will highlight their interesting decision-theoretic connections to conventional estimators, and briefly discuss our on-going work in that area. I will then conclude the talk with some remarks on future research directions that have the potential to make an impact across statistics as a whole.
Abstract: Rare, low-probability events often lead to the biggest impacts. Therefore, the development of cutting-edge statistical machine learning approaches for modeling, predicting and quantifying risks is of utmost importance in a variety of fields of applications. Climate scientists, insurers, engineers, and financial analysts have indeed realized that the greatest risks are often caused by changes in the intensity, frequency, extent, and persistence of extreme events, rather than changes in their average behavior. However, while datasets are often massive in modern-day applications, extreme events are always scarce by nature. This makes it doubly challenging: models needed to realistically describe the dependence structure of high-dimensional random vectors are becoming increasingly complex, but the number of independent replicates used to fit these models remains relatively small. It is thus very important to design specialized models with strong theoretical support for reliable extrapolation to yet-unseen risk levels, as well as efficient inference methods to fit them to big datasets. In this colloquium, I will first provide a quick overview of classical models for spatial extremes and their severe methodological and computational limitations. I will then describe recent progress we have made to develop novel sub-asymptotic spatial models with an improved flexibility in their tail structure. To overcome computational challenges when performing inference, I will then discuss neural Bayes estimators, which are general, amortized, likelihood-free estimators constructed from permutation-invariant neural networks, that we recently developed for near-optimal and fast inference in complex models. Post-training, these estimators allow estimation of model parameters and uncertainty quantification in just a fraction of second. I will highlight their interesting decision-theoretic connections to conventional estimators, and briefly discuss our on-going work in that area. I will then conclude the talk with some remarks on future research directions that have the potential to make an impact across statistics as a whole.
Practical information
- Informed public
- Free
- This event is internal
Organizer
- Institute of Mathematics
Contact
- Prof. Maryna Viazovska, Director