Weak Signals: Machine Learning Meets Extreme Value Theory

Explore the intersection of machine learning and extreme value theory in this 55-minute lecture by Stephan Clemençon at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the concept of angular measure on the unit sphere and its role in characterizing first-order dependence structures of random vector components in extreme regions. Examine the challenges of statistical recovery using rank transformation for standardizing data with different component distributions. Discover finite-sample bounds for maximal deviations between empirical and true angular measures, and learn how these bounds apply to binary classification and unsupervised anomaly detection in extreme regions. Gain insights into performance guarantees for statistical learning procedures built upon empirical angular measure, including empirical risk minimization and minimum-volume sets on the sphere.