pith. sign in

arxiv: 1712.02747 · v2 · pith:K7TJAW3Cnew · submitted 2017-12-07 · 🧮 math.ST · stat.TH

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

Olivier Catoni , Ilaria Giulini This is my paper
classification 🧮 math.ST stat.TH
keywords boundsdimension-freeestimationleastlinearmatricespac-bayesianregression
0
0 comments X
read the original 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.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. A Unified Approach to Robust Mean Estimation

    stat.ML 2019-07 unverdicted novelty 7.0

    A connection between Huber's contamination and heavy-tailed models yields unified robust mean estimators that are both computationally efficient and statistically optimal under certain conditions.

  2. Distribution-robust mean estimation via smoothed random perturbations

    math.ST 2019-06 unverdicted novelty 7.0

    New smoothed random-perturbation estimators for the mean achieve exponential concentration bounds using only finite second-moment assumptions.

  3. Error bounds of Median-of-means estimators with VC-dimension

    math.ST 2024-09 unverdicted novelty 6.0

    Derives VC-dimension-based error bounds for MOM mean estimators and introduces MOM halfspace depth estimator under finite second moment assumptions.