NeurIPS workshop paper derives closed-form Hilbert metric for the SPD bicone of extended Gaussians
FrnkNlsn · x · 2026-09-30
The paper "Hilbert geometry of the symmetric positive-definite bicone" by Jacek Karwowski and Frank Nielsen appears in the NeurIPS Workshops on Symmetry and Geometry in Neural Representations proceedings (PMLR 282:263-281).
- The extended Gaussian family is the closure of the Gaussian family under degenerate covariance/precision; its parameter space forms an SPD semi-definite matrix bicone
- The paper reports a closed-form formula for the Hilbert metric distance on this open bounded convex bicone and studies its invariance properties exhaustively
- Potential applications to handling extended Gaussian distributions are discussed
The PDF is freely available via the PMLR page.
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