Stochastic Wasserstein Barycenters
By Sebastian Claici, Edward Chien, Justin Solomon. 2018
79 citations recorded by the source corpus.
We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport. Unlike previous approaches, our method extends to continuous input distributions and allows the support of the barycenter to be adjusted in each iteration. We tackle the problem without regularization, allowing us to recover a sharp output whose support is contained within the support of the true barycenter. We give examples where our algorithm recovers a more meaningful barycenter than previous work. Our method is versatile and can be extended to applications such as generating super samples from a given distribution and recovering blue noise approximations.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Statistical and Nonlinear Physics, Probabilistic & Bayesian Methods, Mathematical Optimization
Citations in the corpus
- GAIT: A Geometric Approach to Information Theory (2019, neutral): “…the approximation of the density of a mixture of Gaussians P by a uniform distribution Q = 1N ∑N i=1 δxi over N = 200 atoms with a polynomial kernel of degree 1.5, similar to the approximate super-samples (Chen et al., 2010) task presented by Claici et al. (2018) using the Wasserstein distance.”
- Decentralize and Randomize: Faster Algorithm for Wasserstein Barycenters (2018, unknown): “[11, 6, 13] × × √ [22] × √ × [43, 10] × √ √ OUR ALG.”
- Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithm (2019, unknown): “The first problem is typically addressed by either fixing the support of the barycenter a-priori [20, 50] or by adopting an alternating minimization procedure to iteratively optimize the support point locations and their weights [12, 14].”
- A Fast Proximal Point Method for Computing Exact Wasserstein Distance (2018, unknown): “We are also aware of that there are other literatures for Wassersetin barycenter, such as [38] and [7], but they are targeting a more complicated setting, and has a different convergence rate (i.”