Strong Gaussian Approximation for the Sum of Random Vectors
Abstract
This paper derives a new strong Gaussian approximation bound for the sum of independent random vectors. The approach relies on the optimal transport theory and yields explicit dependence on the dimension size p and the sample size n. This dependence establishes a new fundamental limit for all practical applications of statistical learning theory. Particularly, based on this bound, we prove approximation in distribution for the maximum norm in a high-dimensional setting (p > n).
Cite
Text
Buzun et al. "Strong Gaussian Approximation for the Sum of Random Vectors." Conference on Learning Theory, 2022.Markdown
[Buzun et al. "Strong Gaussian Approximation for the Sum of Random Vectors." Conference on Learning Theory, 2022.](https://mlanthology.org/colt/2022/buzun2022colt-strong/)BibTeX
@inproceedings{buzun2022colt-strong,
title = {{Strong Gaussian Approximation for the Sum of Random Vectors}},
author = {Buzun, Nazar and Shvetsov, Nikolay and Dylov, Dmitry V.},
booktitle = {Conference on Learning Theory},
year = {2022},
pages = {1693-1715},
volume = {178},
url = {https://mlanthology.org/colt/2022/buzun2022colt-strong/}
}