Strong Gaussian Approximation for the Sum of Random Vectors

Nazar Buzun, Nikolay Shvetsov, Dmitry V. Dylov
Proceedings of Thirty Fifth Conference on Learning Theory, PMLR 178:1693-1715, 2022.

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 this Paper

BibTeX
@InProceedings{pmlr-v178-buzun22a, title = {Strong Gaussian Approximation for the Sum of Random Vectors}, author = {Buzun, Nazar and Shvetsov, Nikolay and Dylov, Dmitry V.}, booktitle = {Proceedings of Thirty Fifth Conference on Learning Theory}, pages = {1693--1715}, year = {2022}, editor = {Loh, Po-Ling and Raginsky, Maxim}, volume = {178}, series = {Proceedings of Machine Learning Research}, month = {02--05 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v178/buzun22a/buzun22a.pdf}, url = {https://proceedings.mlr.press/v178/buzun22a.html}, 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).} }
Endnote
%0 Conference Paper %T Strong Gaussian Approximation for the Sum of Random Vectors %A Nazar Buzun %A Nikolay Shvetsov %A Dmitry V. Dylov %B Proceedings of Thirty Fifth Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2022 %E Po-Ling Loh %E Maxim Raginsky %F pmlr-v178-buzun22a %I PMLR %P 1693--1715 %U https://proceedings.mlr.press/v178/buzun22a.html %V 178 %X 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).
APA
Buzun, N., Shvetsov, N. & Dylov, D.V.. (2022). Strong Gaussian Approximation for the Sum of Random Vectors. Proceedings of Thirty Fifth Conference on Learning Theory, in Proceedings of Machine Learning Research 178:1693-1715 Available from https://proceedings.mlr.press/v178/buzun22a.html.

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