Sampling From the Wasserstein Barycenter
arXiv:2105.01706
Abstract
This work presents an algorithm to sample from the Wasserstein barycenter of absolutely continuous measures. Our method is based on the gradient flow of the multimarginal formulation of the Wasserstein barycenter, with an additive penalization to account for the marginal constraints. We prove that the minimum of this penalized multimarginal formulation is achieved for a coupling that is close to the Wasserstein barycenter. The performances of the algorithm are showcased in several settings.
References in corpus (9)
- Fast Computation of Wasserstein Barycenters
- Gradient descent algorithms for Bures-Wasserstein barycenters
- Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices
- Wasserstein barycenters are NP-hard to compute
- Exponential ergodicity of mirror-Langevin diffusions
- Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithm
- Averaging Atmospheric Gas Concentration Data using Wasserstein Barycenters
- SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence
- Sinkhorn Barycenter via Functional Gradient Descent