Continuous Regularized Wasserstein Barycenters

Optimal Transport

Cite Paper Code

Authors

Lingxiao Li
Aude Genevay
Mikhail Yurochkin
Justin Solomon

Categories

NeurIPS Optimal Transport

Wasserstein barycenters provide a geometrically meaningful way to aggregate probability distributions, built on the theory of optimal transport. They are difficult to compute in practice, however, leading previous work to restrict their supports to finite sets of points. Leveraging a new dual formulation for the regularized Wasserstein barycenter problem, we introduce a stochastic algorithm that constructs a continuous approximation of the barycenter. We establish strong duality and use the corresponding primal-dual relationship to parametrize the barycenter implicitly using the dual potentials of regularized transport problems. The resulting problem can be solved with stochastic gradient descent, which yields an efficient online algorithm to approximate the barycenter of continuous distributions given sample access. We demonstrate the effectiveness of our approach and compare against previous work on synthetic examples and real-world applications.

This paper has been published as a poster at the 2020 Neural Information Processing Systems (NeurIPS) conference.

Please cite our work using the BibTeX below.

@misc{li2020continuous,
      title={Continuous Regularized Wasserstein Barycenters}, 
      author={Lingxiao Li and Aude Genevay and Mikhail Yurochkin and Justin Solomon},
      year={2020},
      eprint={2008.12534},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}