Lower Bounds on the Total Variation Distance Between Mixtures of Two Gaussians
Probability
2022-03-11 v2 Information Theory
Machine Learning
math.IT
Statistics Theory
Statistics Theory
Abstract
Mixtures of high dimensional Gaussian distributions have been studied extensively in statistics and learning theory. While the total variation distance appears naturally in the sample complexity of distribution learning, it is analytically difficult to obtain tight lower bounds for mixtures. Exploiting a connection between total variation distance and the characteristic function of the mixture, we provide fairly tight functional approximations. This enables us to derive new lower bounds on the total variation distance between pairs of two-component Gaussian mixtures that have a shared covariance matrix.
Keywords
Cite
@article{arxiv.2109.01064,
title = {Lower Bounds on the Total Variation Distance Between Mixtures of Two Gaussians},
author = {Sami Davies and Arya Mazumdar and Soumyabrata Pal and Cyrus Rashtchian},
journal= {arXiv preprint arXiv:2109.01064},
year = {2022}
}
Comments
22 pages, 1 figure; Accepted to ALT 2022