Computationally simpler or faster kernels with the axiomatic guarantees

Identify other radial kernels that retain the monotonicity, uniqueness, and continuity guarantees of canonical Geometric Kernel Diversity while enabling simpler or faster computation.

Background

The paper proves the three axioms for Geometric Kernel Diversity under a broad class of completely monotone radial kernels with accumulating Laplace support, and specializes to a Student-t2 kernel because it enables exact algorithms in dimensions at most three and efficient sampling in arbitrary dimensions.

The authors leave unresolved whether another kernel in the axiomatic class could provide computational advantages over the canonical Student-t2 choice, particularly simpler exact evaluations or faster algorithms.