New paper: two tales of the geometric Jensen-Shannon divergence as JSD regularizations
FrnkNlsn · x · 2026-09-04
Frank Nielsen's paper (arXiv:2508.05066, 28 pages) studies the geometric Jensen-Shannon divergence (G-JSD):
- Introduces an extended G-JSD for positive densities that skips normalizing geometric mixtures, generalizing to positive measures, with the gap to the original G-JSD made explicit.
- Proves the extended G-JSD is an f-divergence satisfying information monotonicity and information-geometric invariance, expressible via the Jeffreys divergence and Bhattacharyya distance/coefficient.
- Derives closed forms for both variants under multivariate Gaussians, plus Monte Carlo estimation via projective γ-divergences.
- Shows that while sqrt(JSD) is a metric, this fails for both G-JSDs; both can be read as regularizations of the ordinary JSD.
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