A Smoothed Dual Approach for Variational Wasserstein Problems

03/09/2015
by   Marco Cuturi, et al.
0

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.

READ FULL TEXT

page 17

page 18

page 19

research
11/13/2018

Semi-dual Regularized Optimal Transport

Variational problems that involve Wasserstein distances and more general...
research
10/09/2022

Coresets for Wasserstein Distributionally Robust Optimization Problems

Wasserstein distributionally robust optimization () is a popular model t...
research
04/24/2018

Data-driven regularization of Wasserstein barycenters with an application to multivariate density registration

We present a framework to simultaneously align and smooth data in the fo...
research
02/24/2020

Variational Wasserstein Barycenters for Geometric Clustering

We propose to compute Wasserstein barycenters (WBs) by solving for Monge...
research
11/15/2019

The quadratic Wasserstein metric for inverse data matching

This work characterizes, analytically and numerically, two major effects...
research
07/04/2023

Wasserstein medians: robustness, PDE characterization and numerics

We investigate the notion of Wasserstein median as an alternative to the...
research
12/02/2018

Regularized Wasserstein Means Based on Variational Transportation

We raise the problem of regularizing Wasserstein means and propose sever...

Please sign up or login with your details

Forgot password? Click here to reset