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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.
Information and information stability of random variables and processes
M. S. Pinsker · 1964
Earlier work this paper cites.
Note on discrimination information and variation
Igor Vajda · 1970
Earlier work this paper cites.
Asymptotic evaluation of certain Markov process expectations for large time. I. II
M. D. Donsker and S. R. S. Varadhan · 1975
Earlier work this paper cites.
Estimation des densités: risque minimax
J. Bretagnolle and C. Huber · 1978
Earlier work this paper cites.
Integral probability metrics and their generating classes of functions
Alfred Müller · 1997
Cited alongside, same era.
Introduction to nonparametric estimation
Alexandre B. Tsybakov · 2004
Cited alongside, same era.
Generalised pinsker inequalities
Mark D. Reid and Robert C. Williamson · 2009
Cited alongside, same era.
Igal Sason and Sergio Verdú · 2016
Cited alongside, same era.
Two reference requests: Pinsker’s inequality and Pontryagin duality
Ilya Razenshteyn · 2018
Later among the works it cites.
Batched multi-armed bandits problem
Zijun Gao, Yanjun Han, Zhimei Ren, and Zhengqing Zhou · 2019
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Bandit algorithms
T. Lattimore and Cs. Szepesvári · 2020
Later among the works it cites.
Lecture notes on: Information-theoretic methods for high-dimensional statistics
Yihong Wu · 2020
Later among the works it cites.
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