Frank Nielsen shows Bregman divergences can be rewritten as power distances
FrnkNlsn · x · 2026-10-26
A 47-page arXiv paper by Frank Nielsen proves that Bregman divergences between parameters can be expressed as power distances between weighted points, connecting information geometry with computational geometry. Key results: Bregman nearest/farthest neighbor queries reduce to Euclidean queries in one extra dimension; minimum enclosing Bregman balls are equivalent to double-sided weighted power MEBs, with an exact LP-type algorithm and an arbitrarily accurate Frank-Wolfe approximation scheme; and the potential-function lifting for Bregman Voronoi diagrams is reinterpreted as classical paraboloid lifting, linking Bregman Voronoi diagrams to power diagrams.
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