PAC-Bayesian bounds for the Gram matrix and least squares regression with a random design

By Olivier Catoni. 2016

47 citations recorded by the source corpus.

The topics dicussed in this paper take their origin inthe estimation of the Gram matrix of a random vector from a sample made of n independent copies. They comprise the estimation of the covariance matrix and the study of least squares regression with a random design. We propose four types of results, based on non-asymptotic PAC-Bayesian generalization bounds: a new robust estimator of the Gram matrix and of the covariance matrix, new results on the empirical Gram matrix, new robust least squares estimators and new results on the ordinary least squares estimator, including its exact rate of convergence under polynomial moment assumptions.

Subfields: Computational Mechanics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/27caa07425df7d4773ec0ac8c73342088617ce52

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In Computational Mechanics

In Statistics and Probability

Citations in the corpus

Sub-Gaussian estimators of the mean of a random matrix with heavy-tailed entries (2016, background): “For instance, in [Cat16] author constructs a robust estimator of the Gram matrix of a random vector Z ∈ Rd (as well as its covariance matrix) via estimating the quadratic form E 〈Z, u〉(2)”