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