Lower Bounds on the Total Variation Distance Between Mixtures of Two Gaussians
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 twocomponent Gaussian mixtures that have a shared covariance matrix.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.01064
 Bibcode:
 2021arXiv210901064D
 Keywords:

 Mathematics  Probability;
 Computer Science  Information Theory;
 Computer Science  Machine Learning;
 Mathematics  Statistics Theory
 EPrint:
 22 pages, 1 figure