Polynomial-Time Optimal Group Selection via the Double-Commutator Eigenvalue Problem
The algebraic diversity framework generalizes temporal averaging over multiple observations to algebraic group action on a single observation for second-order statistical estimation. The central open problem in this framework is $\textit{group selection}$: given an $M$-dimensional observation with unknown covariance structure, find the finite group whose spectral decomposition best matches the covariance. Naive enumeration of all subgroups of the symmetric group $S_M$ requires exponential time in $M$. We prove that this combinatorial problem reduces to a generalized eigenvalue problem derived from the double commutator of the covariance matrix, yielding a polynomial-time algorithm with co...
| Authors | Mitchell A. Thornton |
|---|---|
| Primary category | cs.LG |
| Published | 4 April 2026 |
| Last updated at source | 8 May 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.