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

Olivier Catoni; Ilaria Giulini

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arXiv · 1712.02747

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

Olivier Catoni·Ilaria Giulini

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Abstract

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.

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Olivier Catoni, Ilaria Giulini. 2017-12-07. Dimension-free PAC-Bayesian bounds for matrices, vectors, and linear least squares regression. https://arxiv.org/abs/1712.02747

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