New log-extrinsic statistics on symmetric cones yield closed-form equivariant means without Riemannian iteration
FrnkNlsn · x · 2026-09-05
A new Information Geometry paper by Trindade, Chevallier, Nielsen and Nicolet introduces a log-extrinsic framework for symmetric cones (SPD matrices, Lorentz cones). Using orbital decomposition, it yields an equivariant closed-form mean requiring only elementary linear algebra — proven to coincide with the Riemannian Fréchet mean under natural symmetry assumptions — plus a matched exponential family of log-extrinsic Gaussians, combining geometric symmetry with scalability.
Related event: New Paper Introduces Equivariant Statistics on Symmetric Cones(2 posts)→
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