Tight Bounds Between the Jensen-Shannon Divergence and the Minmax Divergence.

Arseniy Akopyan, Herbert Edelsbrunner, Žiga Virk, Hubert Wagner

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Article in Entropy (Basel, Switzerland), 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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4 authors.

Arseniy AkopyanFora Capital, Miami, FL 33131, USA.ORCID 0000-0002-2548-617X

Herbert EdelsbrunnerISTA (Institute of Science and Technology Austria), 3400 Klosterneuburg, Austria.

Žiga VirkFaculty of Computer and Information Science, University of Ljubljana, 1000 Ljubljana, Slovenia.ORCID 0000-0001-9016-011X

Hubert WagnerDepartment of Mathematics, University of Florida, Gainesville, FL 32611, USA.

Funding

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6 · The paper itself

Abstract

Motivated by questions arising at the intersection of information theory and geometry, we compare two dissimilarity measures between finite categorical distributions. One is the well-known Jensen-Shannon divergence, which is easy to compute and whose square root is a proper metric. The other is what we call the minmax divergence, which is harder to compute. Just like the Jensen-Shannon divergence, it arises naturally from the Kullback-Leibler divergence. The main contribution of this paper is a proof showing that the minmax divergence can be tightly approximated by the Jensen-Shannon divergence. The bounds suggest that the square root of the minmax divergence is a metric, and we prove that this is indeed true in the one-dimensional case. The general case remains open. Finally, we consider analogous questions in the context of another Bregman divergence and the corresponding Burbea-Rao (Jensen-Bregman) divergence.

Indexed as

boundsBregman divergenceBurbea–Rao divergenceinformation theoryJensen-Bregman divergenceJensen–Shannon divergenceKullback–Leibler divergencemetricminmax divergencerelative entropy

Identifiers

PMID40870326

DOI10.3390/e27080854

PMCPMC12386000

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