Polynomial-Time Optimal Group Selection via the Double-Commutator Eigenvalue Problem
Algebraic diversity framework solves group selection via eigenvalue problems in polynomial time
The algebraic diversity framework replaces temporal averaging over multiple observations with algebraic group action on a single observation for second-order statistical estimation. The central open problem in this framework is $group selection$: given an $M$-dimensional observation with unknown covariance structure, find the finite group whose spectral decomposition best matches the covariance. Naive enumeration of…