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arXiv · 2606.07346

Geometric Factorization of Sufficient Harmonic Representations

Kennon Stewart
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Abstract

For tasks of likelihood families invariant under the action of a lie group, the quotient is the minimal sufficient invariant representation. On compact homogeneous spaces, this quotient representation admits a harmonic realization through spherical Fourier coefficients; for finite-band harmonic exponential families, the empirical harmonic coefficients are minimal sufficient statistics. The partition function can be expressed algebraically by extracting the trivial representation component through Clebsch-Gordan decomposition.

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Kennon Stewart. 2026-06-05. Geometric Factorization of Sufficient Harmonic Representations. https://arxiv.org/abs/2606.07346

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