The total variation distance between high-dimensional Gaussians with the same mean
Statistics Theory
2023-10-24 v7 Probability
Statistics Theory
Abstract
Given two high-dimensional Gaussians with the same mean, we prove a lower and an upper bound for their total variation distance, which are within a constant factor of one another.
Cite
@article{arxiv.1810.08693,
title = {The total variation distance between high-dimensional Gaussians with the same mean},
author = {Luc Devroye and Abbas Mehrabian and Tommy Reddad},
journal= {arXiv preprint arXiv:1810.08693},
year = {2023}
}
Comments
In an earlier version, tight bounds were claimed for the total-variation distance between two general Gaussians. But the proof of the upper bound was incorrect, and we removed the flawed bound from the paper. Later, Arbas, Ashtiani, and Liaw (Theorem 1.8 in arxiv.org/abs/2303.04288v2) proved tight bounds for the total-variation distance between two general Gaussians, solving the original problem