Sliced Wasserstein Barycenter of Multiple Densities
نویسندگان
چکیده
The optimal mass transportation problem provides a framework for interpolating between different probability density functions (pdfs), warping one function toward another. Interpolating between two arbitrary pdfs can be challenging, but interpolating between more than two pdfs just remains untractable. We propose an approximation of such interpolations based on 1D projections, that is efficiently solved via Radon transforms. We observe the expected translational behavior of this interpolation on smooth 2D functions, and prove that it corresponds to the exact interpolant in a few particular cases.
منابع مشابه
Wasserstein Barycenter and Its Application to Texture Mixing
This paper proposes a new definition of the averaging of discrete probability distributions as a barycenter over theWasserstein space. Replacing the Wasserstein original metric by a sliced approximation over 1D distributions allows us to use a fast stochastic gradient descent algorithm. This new notion of barycenter of probabilities is likely to find applications in computer vision where one wa...
متن کاملConsistent estimation of a population barycenter in the Wasserstein space
We define a notion of barycenter for random probability measures in the Wasserstein space. We study the population barycenter in terms of existence and uniqueness. Using a duality argument, we give a precise characterization of the population barycenter for compactly supported measures, and we make a connection between averaging in the Wasserstein space and taking the expectation of optimal tra...
متن کاملBarycenters in the Wasserstein Space
In this paper, we introduce a notion of barycenter in the Wasserstein space which generalizes McCann’s interpolation to the case of more than two measures. We provide existence, uniqueness, characterizations and regularity of the barycenter, and relate it to the multimarginal optimal transport problem considered by Gangbo and Świȩch in [8]. We also consider some examples and in particular rigor...
متن کاملStochastic 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 ...
متن کاملParallel Streaming Wasserstein Barycenters
Efficiently aggregating data from different sources is a challenging problem, particularly when samples from each source are distributed differently. These differences can be inherent to the inference task or present for other reasons: sensors in a sensor network may be placed far apart, affecting their individual measurements. Conversely, it is computationally advantageous to split Bayesian in...
متن کامل