منابع مشابه
Barycenters of Measures Transported by Stochastic Flows
We investigate the evolution of barycenters of masses transported by stochastic flows. The state spaces under consideration are smooth affine manifolds with certain convexity structure. Under suitable conditions on the flow and on the initial measure, the barycenter {Zt} is shown to be a semimartingale and is described by a stochastic differential equation. For the hyperbolic space the barycent...
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 کاملFast Computation of Wasserstein Barycenters
We present new algorithms to compute the mean of a set of empirical probability measures under the optimal transport metric. This mean, known as the Wasserstein barycenter, is the measure that minimizes the sum of its Wasserstein distances to each element in that set. We propose two original algorithms to compute Wasserstein barycenters that build upon the subgradient method. A direct implement...
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...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1972
ISSN: 0022-247X
DOI: 10.1016/0022-247x(72)90007-8