Classification of Heavy-tailed Features in High Dimensions: a Superstatistical Approach
NeurIPS(2023)
摘要
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.
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关键词
superstatistical features,classification
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