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Fast 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 algorit ..."
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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
Gradient flows in metric spaces and in the space of probability measures
 LECTURES IN MATHEMATICS ETH ZÜRICH, BIRKHÄUSER VERLAG
, 2005
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A note on the computation of Wasserstein barycenters.∗
, 2015
"... We consider the problem of finding the barycenter of a finite set of probabilities on Rd with respect to the Wasserstein metric. We introduce an iterative procedure which consistenly approximates the barycenter under general conditions. These cover the case of probabilities in a locationscatter fa ..."
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We consider the problem of finding the barycenter of a finite set of probabilities on Rd with respect to the Wasserstein metric. We introduce an iterative procedure which consistenly approximates the barycenter under general conditions. These cover the case of probabilities in a location
Numerical methods for matching for teams and Wasserstein barycenters
, 2014
"... Equilibrium multipopulation matching (matching for teams) is a problem from mathematical economics which is related to multimarginal optimal transport. A special but important case is the Wasserstein barycenter problem, which has applications in image processing and statistics. Two algorithms a ..."
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Equilibrium multipopulation matching (matching for teams) is a problem from mathematical economics which is related to multimarginal optimal transport. A special but important case is the Wasserstein barycenter problem, which has applications in image processing and statistics. Two algorithms
Noname manuscript No. (will be inserted by the editor) Sliced and Radon Wasserstein Barycenters of Measures
"... the date of receipt and acceptance should be inserted later Abstract This article details two approaches to compute barycenters of measures using 1D Wasserstein distances along radial projections of the input measures. The first method makes use of the Radon transform of the measures, and the seco ..."
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the date of receipt and acceptance should be inserted later Abstract This article details two approaches to compute barycenters of measures using 1D Wasserstein distances along radial projections of the input measures. The first method makes use of the Radon transform of the measures
DOI: 10.1137/100805741 Barycenters in the Wasserstein space
, 2010
"... 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 probl ..."
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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
WASP: Scalable Bayes via barycenters of subset posteriors
"... The promise of Bayesian methods for big data sets has not fully been realized due to the lack of scalable computational algorithms. For massive data, it is necessary to store and process subsets on different machines in a distributed manner. We propose a simple, general, and highly efficient appr ..."
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proach, which first runs a posterior sampling algorithm in parallel on different machines for subsets of a large data set. To combine these subset posteriors, we calculate the Wasserstein barycenter via a highly efficient linear program. The resulting estimate for the Wasserstein posterior (WASP) has
K.: Consistent estimation of a population barycenter in the wasserstein space
, 2012
"... We define a notion of barycenter for random probability measures in the Wasserstein space. We give a characterization of the population barycenter in terms of existence and uniqueness for compactly supported measures. Then, the problem of estimating this barycenter from n independent and identicall ..."
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We define a notion of barycenter for random probability measures in the Wasserstein space. We give a characterization of the population barycenter in terms of existence and uniqueness for compactly supported measures. Then, the problem of estimating this barycenter from n independent
BARYCENTERS OF MEASURES TRANSPORTED BY STOCHASTIC FLOWS
, 2005
"... 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 semimarting ..."
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Cited by 9 (3 self)
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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
The Variational Formulation of the FokkerPlanck Equation
 SIAM J. Math. Anal
, 1999
"... The FokkerPlanck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic differential equation. It pertains to a wide variety of timedependent systems in which randomness plays a role. In this paper, ..."
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Cited by 285 (22 self)
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The FokkerPlanck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic differential equation. It pertains to a wide variety of timedependent systems in which randomness plays a role. In this paper
Results 1  10
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