Selecting diffusion processes to overcome the curse of dimensionality in Stein discrepancies

Identify and develop suitable non-isotropic diffusion processes on R^d that induce kernel Stein discrepancies capable of mitigating the curse of dimensionality, and establish theoretical guidance for the selection of such diffusions in high-dimensional applications.

Background

The performance of Stein discrepancies in high dimensions can suffer due to the curse of dimensionality when isotropic kernels are used. One proposed avenue is to replace the overdamped Langevin diffusion with more general diffusion processes, leading to non-isotropic kernels that may better detect discrepancies in high dimensions.

Although this generalization exists in theory, practical and theoretical guidance on which diffusion processes to choose to effectively address the curse of dimensionality has not been explored, leaving a gap between theory and application.