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arXiv · 2202.07198

A short note on an inequality between KL and TV

Clément L. Canonne
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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.

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Clément L. Canonne. 2022-02-15. A short note on an inequality between KL and TV. https://arxiv.org/abs/2202.07198

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