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

12/07/2017

∙

by   Olivier Catoni, et al.

∙

Young’s fringes pattern obtained at 80 kV showing a point

∙

Ensae ParisTech

∙

0

∙

share

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.