Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernel

arXiv:2310.03054v2 Announce Type: replace-cross
Abstract: We propose conditional flows of the maximum mean discrepancy (MMD) with the negative distance kernel for posterior sampling and conditional generative modeling. This MMD, which is also known as energy distance, has several advantageous properties like efficient computation via slicing and sorting. We approximate the joint distribution of the ground truth and the observations using discrete Wasserstein gradient flows and establish an error bound for the posterior distributions. Further, we prove that our particle flow …

abstract arxiv computation cs.lg energy generative generative modeling gradient kernel math.oc math.pr mean modeling negative posterior sampling slicing sorting stat.ml type via