122 citations · 349 across the 22 of their papers we have counts for
28 papers
Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels
Matthew Rosenzweig, Dejan Slepčev, Lihan Wang
We study the Wasserstein gradient flow of the squared Maximum Mean Discrepancy (MMD) generated by the nonsmooth energy kernels , . In dimensions , the co…
Radon--Wasserstein Gradient Flows for Interacting-Particle Sampling in High Dimensions
Elias Hess-Childs, Dejan Slepčev, Lantian Xu
Gradient flows of the Kullback--Leibler (KL) divergence, such as the Fokker--Planck equation and Stein Variational Gradient Descent, evolve a distribution toward a target density k…
HV Geometry for Signal Comparison
Ruiyu Han, Dejan Slepčev, Yunan Yang
In order to compare and interpolate signals, we investigate a Riemannian geometry on the space of signals. The metric allows discontinuous signals and measures both horizontal (thu…
Birth-death dynamics for sampling: Global convergence, approximations and their asymptotics
Yulong Lu, Dejan Slepčev, Lihan Wang
Motivated by the challenge of sampling Gibbs measures with nonconvex potentials, we study a continuum birth-death dynamics. We improve results in previous works [51,57] and provide…
Nonlocal Wasserstein Distance: Metric and Asymptotic Properties
Dejan Slepčev, Andrew Warren
The seminal result of Benamou and Brenier provides a characterization of the Wasserstein distance as the path of the minimal action in the space of probability measures, where path…
Boundary Estimation from Point Clouds: Algorithms, Guarantees and Applications
Jeff Calder, Sangmin Park, Dejan Slepčev
We investigate identifying the boundary of a domain from sample points in the domain. We introduce new estimators for the normal vector to the boundary, distance of a point to the…