Frank Nielsen's duo Bregman divergence paper unifies KL across exponential families
FrnkNlsn · x · 2026-09-20
Frank Nielsen highlights his paper 'The duo Bregman and Fenchel-Young divergences' (arXiv:2202.10726, Entropy 2022). Computing KL divergence between measures from different exponential families yields a formula generalizing Fenchel-Young divergence; the duo Fenchel-Young divergence is shown equivalent to a duo Bregman divergence, with a majorization condition ensuring non-negativity. Applications include KL between nested exponential families, a formula for truncated normals, and showing skewed Bhattacharyya distance equals a skewed duo Jensen divergence.
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