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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
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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
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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
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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
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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
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Exponential ergodicity of mirror-Langevin diffusions
TLDR
We propose a class of diffusions called Newton-Langevin diffusions and prove 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
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Projection to Fairness in Statistical Learning.
TLDR
In the context of regression, we consider the fundamental question of making an estimator fair while preserving its prediction accuracy as much as possible. Expand
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Fast convergence of empirical barycenters in Alexandrov spaces and the Wasserstein space
This work establishes fast rates of convergence for empirical barycenters over a large class of geodesic spaces with curvature bounds in the sense of Alexandrov. More specifically, we show thatExpand
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Unconstrained and Curvature-Constrained Shortest-Path Distances and Their Approximation
TLDR
We study shortest paths and their distances on a subset of a Euclidean space, and their approximation by their equivalents in a neighborhood graph defined on a sample from that subset. Expand
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