A short note on an inequality between KL and TV
Probability
2023-08-03 v2 Statistics Theory
Statistics Theory
Abstract
The goal of this short note is to discuss the relation between Kullback--Leibler divergence and total variation distance, starting with the celebrated Pinsker's inequality relating the two, before switching to a simple, yet (arguably) more useful inequality, apparently not as well known, due to Bretagnolle and Huber. We also discuss applications of this bound for minimax testing lower bounds.
Cite
@article{arxiv.2202.07198,
title = {A short note on an inequality between KL and TV},
author = {Clément L. Canonne},
journal= {arXiv preprint arXiv:2202.07198},
year = {2023}
}
Comments
Update: positive answer to Question 8 ("from the TFL to the BH bound"), communicated to me by Hao-Chung Cheng