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

2017/12/07 by Olivier Catoni, Catoni, Olivier, Ilaria Giulini +1 · 4 citations
Engineering · Mathematics · #15B52 #62F35 #62H12 #62H20 #62J05 #62J10 #Advanced Statistical Methods and Models #FOS: Mathematics #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1712.02747

openalex publication_date 2017/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Relative Information Gain and Gaussian Process Regression
• Learning via Wasserstein-Based High Probability Generalisation Bounds
• A variational approach to dimension-free self-normalized concentration
• Fast Mean Estimation with Sub-Gaussian Rates

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