New arXiv paper proves group invariance of f-divergences and Fisher-Rao distance reduction
FrnkNlsn · x · 2026-09-29
Frank Nielsen and Kazuki Okamura posted an arXiv paper, "Group invariance of f-divergences and the Fisher-Rao distance" (15 pages).
- Studying how natural symmetries (group actions) in statistical models affect distribution comparison: under a transformation model where a group acts on both sample and parameter spaces with multiplier-transformed densities, every f-divergence is invariant under the group action
- Consequence: an invariant divergence depends only on a maximal invariant of the parameter pair; when the action is transitive, this is given by a double coset
- Applied to multidimensional location-scale families, the same reduction extends to the Fisher-Rao distance
A fundamental result in information geometry and statistical information theory.
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