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 via a double-stochastic process, where the sample is obtained from a Gaussian distribution whose variance is itself a random parameter sampled from a scalar distribution ϱ. As a result, our analysis covers a large family of data distributions, including the case of power-law-tailed distributions with no covariance, and allows us to test recent ''Gaussian universality'' claims. We study the generalisation performance of the obtained estimator, we analyse the role of regularisation, and we analytically characterise the separability transition.

Urte Adomaityte, G.S. (2023). Classification of Heavy-tailed Features in High Dimensions: a Superstatistical Approach.

Classification of Heavy-tailed Features in High Dimensions: a Superstatistical Approach

Gabriele Sicuro;
2023

Abstract

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 via a double-stochastic process, where the sample is obtained from a Gaussian distribution whose variance is itself a random parameter sampled from a scalar distribution ϱ. As a result, our analysis covers a large family of data distributions, including the case of power-law-tailed distributions with no covariance, and allows us to test recent ''Gaussian universality'' claims. We study the generalisation performance of the obtained estimator, we analyse the role of regularisation, and we analytically characterise the separability transition.
2023
Advances in Neural Information Processing Systems 36 (NeurIPS 2023)
43880
43893
Urte Adomaityte, G.S. (2023). Classification of Heavy-tailed Features in High Dimensions: a Superstatistical Approach.
Urte Adomaityte, Gabriele Sicuro, Pierpaolo Vivo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/965238
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