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Existence and consistency of Wasserstein barycenters
Based on the Fréchet mean, we define a notion of barycenter corresponding to a usual notion of statistical mean. We prove the existence of Wasserstein barycenters of random probabilities defined on aExpand
Distribution's template estimate with Wasserstein metrics
In this paper we tackle the problem of comparing distributions of random variables and defining a mean pattern between a sample of random events. Using barycenters of measures in the WassersteinExpand
On the mean speed of convergence of empirical and occupation measures in Wasserstein distance
In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider occupation measuresExpand
SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence
TLDR
A new perspective on SVGD is introduced that views SVGD as the (kernelized) gradient flow of the chi-squared divergence which exhibits a strong form of uniform exponential ergodicity under conditions as weak as a Poincare inequality and proposes an alternative to SVGD, called Laplacian Adjusted Wasserstein Gradient Descent (LAWGD), that can be implemented from the spectral decomposition of the Laplacan operator associated with the target density. Expand
Convergence rates for empirical barycenters in metric spaces: curvature, convexity and extendable geodesics
This paper provides rates of convergence for empirical (generalised) barycenters on compact geodesic metric spaces under general conditions using empirical processes techniques. Our main assumptionExpand
Projection to Fairness in Statistical Learning.
TLDR
The methodology leverages tools from optimal transport to construct efficiently the projection to fairness of any given estimator as a simple post-processing step, and precisely quantifies the cost of fairness, measured in terms of prediction accuracy. Expand
On the rate of convergence of empirical barycentres in metric spaces: curvature, convexity and extendible geodesics
This paper provides rates of convergence for empirical (generalised) barycenters on compact geodesic metric spaces under general conditions using empirical processes techniques. Our main assumptionExpand
Exponential ergodicity of mirror-Langevin diffusions
TLDR
A class of diffusions called Newton-Langevin diffusions are proposed and it is proved that they converge to stationarity exponentially fast with a rate which not only is dimension-free, but also has no dependence on the target distribution. Expand
Optimal dimension dependence of the Metropolis-Adjusted Langevin Algorithm
TLDR
The upper bound proof introduces a new technique based on a projection characterization of the Metropolis adjustment which reduces the study of MALA to the well-studied discretization analysis of the Langevin SDE and bypasses direct computation of the acceptance probability. Expand
Fast convergence of empirical barycenters in Alexandrov spaces and the Wasserstein space
This work establishes fast, i.e., parametric, rates of convergence for empirical barycenters over a large class of geodesic spaces with curvature bounds in the sense of Alexandrov. More specifically,Expand
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