A Smoothed Dual Approach for Variational Wasserstein Problems
Cuturi, Marco; Peyré, Gabriel (2015), A Smoothed Dual Approach for Variational Wasserstein Problems, SIAM Journal on Imaging Sciences, 9, 1, p. 320-343. 10.1137/15M1032600
TypeArticle accepté pour publication ou publié
Journal nameSIAM Journal on Imaging Sciences
Society for Industrial and Applied Mathematics
MetadataShow full item record
Abstract (EN)Variational problems that involve Wasserstein distances have been recently proposed to summarize and learn from probability measures. Despite being conceptually simple, such problems are computationally challenging because they involve minimizing over quantities (Wasserstein distances) that are themselves hard to compute. We show that the dual formulation of Wasserstein variational problems introduced recently by Carlier et al. (2014) can be regularized using an entropic smoothing, which leads to smooth, differentiable, convex optimization problems that are simpler to implement and numerically more stable. We illustrate the versatility of this approach by applying it to the computation of Wasserstein barycenters and gradient flows of spacial regularization functionals.
Subjects / Keywordsconvex optimization; Wasserstein; entropy; Optimal transport
Showing items related by title and author.
Benamou, Jean-David; Carlier, Guillaume; Cuturi, Marco; Nenna, Luca; Peyré, Gabriel (2015) Article accepté pour publication ou publié
Solomon, Justin; De Goes, Fernando; Peyré, Gabriel; Cuturi, Marco; Butscher, Adrian; Nguyen, Andy; Du, Tao; Guibas, Leonidas (2015) Article accepté pour publication ou publié