Kick-off event: AI and the future of mathematics and physics - 21.10.2026
In light of recent developments, the incoming kick-off event at the Institut Henri Poincaré will take the form of a debate gathering mathematicians and theoretical physicists around the role of AI in the practice of research. More information will come soon.
Classification of fat-tailed clusters in high dimensions
byGabriele Sicuro
Abstract:I will discuss the problem of learning a mixture of two clouds of data points with generic centroids via empirical risk minimisation in the high dimensional regime, under the assumptions of generic convex loss and convex regularisation. Each cloud of data points is obtained by sampling from a possibly uncountable superposition of Gaussian distributions, whose variance has a generic probability density ϱ. Our analysis covers therefore a large family of data distributions, including the case of power-law-tailed distributions with no covariance. We study the generalisation performance of the obtained estimator, we analyse the role of regularisation and the dependence of the separability transition on the distribution scale parameters.