Frank Nielsen paper: α-divergences of unnormalized exponential-family densities equal partition-function Jensen divergences
FrnkNlsn · x · 2026-11-12
Frank Nielsen highlights his arXiv paper (2312.12849) showing that KL divergence between unnormalized densities of an exponential family equals the reverse Bregman divergence induced by the partition function (which is log-convex), and that α-divergences correspond to scaled α-skewed Jensen divergences induced by the partition function. The paper also uses comparative convexity over quasi-arithmetic means to deform convex functions and arguments, defining dually flat spaces with associated divergences.
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