EXtremes, STatistical learning and Applications – EXSTA

Extreme Value Theory (EVT) is the branch of probability and statistics concerned with rare events associated with distributional tails, with numerous applications in various scientific fields where extreme events are of special interest, and in risk management. The most recent years have seen an increasing interest towards statistical learning viewpoints on EVT and machine learning algorithms incorporating EVT in large scale applications, resonating with a continued effort of the statistical community to address larger dimensional problems with computationally feasible approaches.

The aim of this project is to reinforce emerging research directions towards this end and to foster interactions between learning theory and practice. The project involves a wide consortium of statisticians with research interests ranging from mathematical statistics and statistical learning theory, to statistical applications and operational use in climate science, risk management and industry.

The research program is organized along two main axes, each of them including theoretical and applied challenges, (I) Unsupervised problems in EVT, (II) Supervised problems. Axis (I) includes the following tasks : 1) Unsupervised dimension reduction and learning sparse representation of the distribution of extremes, with multivariate, temporal and functional data ; 2) Learning multivariate extreme quantiles with novel approaches based on data depth and optimal transport ; 3) Neural Networks and extremes: implementation for the purpose of generating extreme events and approximation guarantees ; 4) Applications to pattern recognition in extreme weather events and simulation of extreme weather in the context of climate change ; 5) Applications to industrial problems related to Anomaly detection and Predictive maintenance. Axis (II) gathers supervised learning tasks involving extremes: 6) Extreme quantile regression and supervised dimension reduction for prediction of extreme events with high dimensional covariates ; 7) Adaptation of supervised learning algorithms for classification and regression tasks when the focus is on extreme covariates and derivation of finite sample guarantees ; 8) Applications to prediction of extreme rainfalls and flood risk in a warming climate.

The intended impacts of this project include, in addition to scientific publications, open source software development under the form of easily reusable off-the-shelf implementations of the novel proposed methodologies, partly supported by engineering teams in partner institutions and in relation with industrial and research chairs in which project members are involved.

The financial support requested will fund three PhD theses of three years each, two workshops, travel expenses, and means for knowledge transfer and dissemination of results.