DeepAI AI Chat
Log In Sign Up

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

by   Olivier Catoni, et al.
Young’s fringes pattern obtained at 80 kV showing a point
Ensae ParisTech

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.


page 1

page 2

page 3

page 4


Dimension-free PAC-Bayesian bounds for the estimation of the mean of a random vector

In this paper, we present a new estimator of the mean of a random vector...

Simpler PAC-Bayesian Bounds for Hostile Data

PAC-Bayesian learning bounds are of the utmost interest to the learning ...

Dimension-free Bounds for Sum of Dependent Matrices and Operators with Heavy-Tailed Distribution

We study the deviation inequality for a sum of high-dimensional random m...

Improved PAC-Bayesian Bounds for Linear Regression

In this paper, we improve the PAC-Bayesian error bound for linear regres...

ℓ_1-regression with Heavy-tailed Distributions

In this paper, we consider the problem of linear regression with heavy-t...

Moment bounds for autocovariance matrices under dependence

The goal of this paper is to obtain expectation bounds for the deviation...

Semi-Infinite Linear Regression and Its Applications

Finite linear least squares is one of the core problems of numerical lin...