Classification of Superstatistical Features in High Dimensions

TY - CHAP

T1 - Classification of Superstatistical Features in High Dimensions

AU - Adomaityte, Urte

AU - Sicuro, Gabriele

AU - Vivo, Pierpaolo

PY - 2023/9/21

Y1 - 2023/9/21

N2 - We characterise the learning of 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.

AB - We characterise the learning of 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.

M3 - Conference paper

BT - 2023 Conference on Neural Information Processing Systems

ER -