On Relations Between Tight Bounds for Symmetric $f$-Divergences and Binary Divergences
Information Theory
2022-11-11 v2 math.IT
Statistics Theory
Statistics Theory
Abstract
Minimizing divergence measures under a constraint is an important problem. We derive a sufficient condition that binary divergence measures provide lower bounds for symmetric divergence measures under a given triangular discrimination or given means and variances. Assuming this sufficient condition, the former bounds are always tight, and the latter bounds are tight when two probability measures have the same variance. An application of these results for nonequilibrium physics is provided.
Keywords
Cite
@article{arxiv.2210.09571,
title = {On Relations Between Tight Bounds for Symmetric $f$-Divergences and Binary Divergences},
author = {Tomohiro Nishiyama},
journal= {arXiv preprint arXiv:2210.09571},
year = {2022}
}
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7 pages