Frank Nielsen surveys recent interpretations and generalizations of Bregman divergences
FrnkNlsn · x · 2026-09-25
Information geometry researcher Frank Nielsen rounds up recent interpretations and generalizations of Bregman divergences:
- Generalization chain: Functional Bregman divergences → Kernelized BD → Deformed MMD, detailed in "Generalising maximum mean discrepancy: kernelised functional Bregman divergences" (with Russell Tsuchida)
- Polar Fenchel-Young divergences, derived from the canonical Legendre polarity via quadratic polarity
- Bregman divergences as power distances
The page also lists related recent work: equivariant log-extrinsic means on symmetric cones, geometric Jensen-Shannon divergence between Gaussians on Hilbert space, simplified minimum enclosing Bregman balls, group invariance of f-divergences and the Fisher-Rao distance, spanning information geometry, computational convexity, and ML.
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