Convergence control for sliced kernel Stein discrepancies

Establish convergence control (for example, weak convergence control in the sense that the discrepancy vanishes if and only if the empirical approximation converges weakly to the target) for sliced kernel Stein discrepancies constructed for high-dimensional targets, by determining appropriate conditions and kernels under which these discrepancies reliably bound an integral probability metric between the target distribution and the empirical approximation.

Background

Kernel Stein discrepancies provide computable bounds on approximation error between MCMC output and a target distribution and are used as diagnostics and for post-processing. Recent work introduced sliced kernel Stein discrepancies to improve scalability in high dimensions, but rigorous convergence guarantees analogous to those established for standard kernel Stein discrepancies have not yet been obtained.

The authors emphasize that without established convergence control, sliced kernel Stein discrepancies cannot presently be relied upon to certify that sampler output approximates the target distribution in a precise sense.