Maximum Mean Discrepancy flows

August 21, 2016 — March 1, 2024

approximation
functional analysis
Hilbert space
measure
metrics
nonparametric
optimization
probability
statistics

Vague question: Can we construct something like a denoising diffusion or other transport maps via the Maximum Mean Discrepancy?

Arbel et al. (2019) looks pertinent and has some connections to Wasserstein gradient flow, which is a thing.

1 References

Arbel, Korba, Salim, et al. 2019. Maximum Mean Discrepancy Gradient Flow.” In Proceedings of the 33rd International Conference on Neural Information Processing Systems.
Chen, Mustafi, Glaser, et al. 2024. (De)-Regularized Maximum Mean Discrepancy Gradient Flow.”
Deep MMD Gradient Flow Without Adversarial Training.” 2024. In.
Hamzi, and Owhadi. 2021. Learning Dynamical Systems from Data: A Simple Cross-Validation Perspective, Part I: Parametric Kernel Flows.” Physica D: Nonlinear Phenomena.