Consistent estimation of a population barycenter in the Wasserstein space

By Jérémie Bigot, Thierry Klein. 2013

62 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/185e0ef06165cb65dd75ba290921d7c467159e37

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Citations in the corpus

Statistical inference for Bures–Wasserstein barycenters (2019, background): “For more details on general optimal transportation maps see Brenier [1991], for a particular case of scale-location families one may refer to Álvarez-Esteban et al.”
Sliced and Radon Wasserstein Barycenters of Measures (2014, unknown): “These barycenters have found application, for instance, in statistical estimation [6].”
Fréchet means and Procrustes analysis in Wasserstein space (2017, background): “We choose this setting since it has a long history in assessing compatibility and fit of distributions related via deformations (Munk & Czado [56]; Freitag & Munk [34]), and as it can be seen to be a natural analogue of using L2, in the case of measures1 (Panaretos & Zemel [61]; Bigot & Klein [14]).”
Wasserstein Barycenters over Riemannian manifolds (2014, background): “Let us note that in addition to economics [8], Wasserstein barycenters in the multi-measure setting have appeared in the literature with applications in image processing [34] and statistics [4].”
Existence and consistency of Wasserstein barycenters (2015, background): “In [9] this problem is also tackled in the particular case where the (μ j ) j≥1 have compact support, are absolutely continuous with respect to the Lebesgue measure and are indexed on a compact set of Rd .”
Iterative Bregman Projections for Regularized Transportation Problems (2014, background): “ces) over the space of measures, which is studied in details in [2]. OT barycenters nd applications for instance in statistics to dene a mean empirical estimator from a family of observed histograms [10], or in machine learning [27] to provide an extended denition of k-means clustering and compute a”
Bayesian Learning with Wasserstein Barycenters (2018, methodology): “Given p ∈ P(Θ) a prior distribution over a parameter space Θ, its push forward Bogachev [2007] through the map T is the probability measure Π = T (p) given by Π(A) = p(T −1(A)).”
Multi-marginal optimal transport: theory and applications (2014, background): “These include texture mixing in image processing, where the aim is to interpolate among several textures (encoded as measures) in order to synthesize a new one [69], and statistics, where the basic goal is to find an average among several distributions while preserving relevant features of them [6].”