Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 59, Issue 11, Pages 7118-7131Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2013.2274515
Keywords
Coupling; entropy; local distance; Stein's method; total variation distance
Funding
- Israel Science Foundation [12/12]
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This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal coupling, and they apply to discrete random variables which are defined over finite or countably infinite alphabets. Loosened versions of these bounds are demonstrated to reproduce some previously reported results. The use of the new bounds is exemplified for the Poisson approximation, where bounds on the local and total variation distances follow from Stein's method.
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