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Pré-Publication, Document De Travail Année : 2021

Dimension-free PAC-Bayesian bounds for matrices, vectors, and linear least squares regression

Résumé

This paper is focused on dimension-free PAC-Bayesian bounds, under weak polynomial moment assumptions, allowing for heavy tailed sample distributions. It covers the estimation of the mean of a vector or a matrix, with applications to least squares linear regression. Special efforts are devoted to the estimation of Gram matrices, due to their prominent role in high-dimension data analysis.

Dates et versions

hal-03196144 , version 1 (12-04-2021)

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Olivier Catoni, Ilaria Giulini. Dimension-free PAC-Bayesian bounds for matrices, vectors, and linear least squares regression. 2021. ⟨hal-03196144⟩
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