Continuous Regularized Wasserstein Barycenters

Abstract

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.

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Cited by in corpus (9)

• Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey
• Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networks
• Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimization
• Averaging on the Bures-Wasserstein manifold: dimension-free convergence of gradient descent
• Score-based Generative Neural Networks for Large-Scale Optimal Transport
• On Transportation of Mini-batches: A Hierarchical Approach
• Fast Topological Clustering with Wasserstein Distance
• A novel notion of barycenter for probability distributions based on optimal weak mass transport
• Variational Wasserstein Barycenters with c-Cyclical Monotonicity