Classification of fat-tailed clusters in high dimensions

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.

mathematical physics

Audience: researchers in the topic

( video )

Seed Seminar of Mathematics and Physics

Series comments: The Seed Seminar hosts talks in mathematics and theoretical physics mainly by young researchers. Zoom link available by registering at our mailing list here