25 research outputs found
Regularized Wasserstein Means for Aligning Distributional Data
We propose to align distributional data from the perspective of Wasserstein
means. We raise the problem of regularizing Wasserstein means and propose
several terms tailored to tackle different problems. Our formulation is based
on the variational transportation to distribute a sparse discrete measure into
the target domain. The resulting sparse representation well captures the
desired property of the domain while reducing the mapping cost. We demonstrate
the scalability and robustness of our method with examples in domain
adaptation, point set registration, and skeleton layout
Stochastic Wasserstein Barycenters
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.Comment: ICML 201