Work

Tight Bounds Between the Jensen–Shannon Divergence and the Minmax Divergence

Year: 2025

Type: article

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.

Source: Entropy

DOI: 10.3390/e27080854

Authors: Arseniy Akopyan, Herbert Edelsbrunner, Žiga Virk, Hubert Wagner

Institutions: Institute of Science and Technology Austria, University of Ljubljana, Institute of Mathematics, Physics, and Mechanics, University of Florida

Language: English

Topic: Statistical Mechanics and Entropy

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: European Commission, Deutsche Forschungsgemeinschaft, Austrian Science Fund