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We propose a new statistical model, the spiked transport model, which formalizes the assumption that two probability distributions differ only on a low-dimensional subspace.
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Wasserstein barycenter and its application to texture mixing
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Learning probability measures with respect to optimal transport metrics
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Optimal detection of sparse principal components in high dimension
Berthet, Q. and Rigollet, P · 2013
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Constructive quantization: approximation by empirical measures
Dereich, S., Scheutzow, M., and Schottstedt, R · 2013
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One-dimensional empirical measures, order statistics and kantorovich transport distances
Bobkov, S. and Ledoux, M · 2014
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On the mean speed of convergence of empirical and occupation measures in Wasserstein distance
Boissard, E. and Le Gouic, T · 2014
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Optimal estimation and rank detection for sparse spiked covariance matrices
Cai, T., Ma, Z., and Wu, Y · 2015
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On the rate of convergence in Wasserstein distance of the empirical measure
Fournier, N. and Guillin, A · 2015
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Computational barriers in minimax submatrix detection
Ma, Z. and Wu, Y · 2015
Entropic optimal transport is maximum-likelihood deconvolution
Rigollet, P. and Weed, J · 2018
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Wasserstein dictionary learning: Optimal transport-based unsupervised nonlinear dictionary learning
Schmitz, M. A., Heitz, M., Bonneel, N., Mboula, F. M. N., Coeurjolly, D., Cuturi, M., Peyré, G., and Starck, J · 2018
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Minimax distribution estimation in Wasserstein distance
Singh, S. and Póczos, B · 2018
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Computational strategies for statistical inference based on empirical optimal transport
Tameling, C. and Munk, A · 2018
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High-dimensional probability , volume 47 of Cambridge Series in Statistical and Probabilistic Mathematics
Vershynin, R · 2018
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Principal geodesic analysis for probability measures under the optimal transport metric
Seguy, V. and Cuturi, M · 2015
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Convolutional wasserstein distances: Efficient optimal transportation on geometric domains
Solomon, J., de Goes, F., Peyré, G., Cuturi, M., Butscher, A., Nguyen, A., Du, T., and Guibas, L · 2015
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Wasserstein training of restricted boltzmann machines
Montavon, G., Müller, K., and Cuturi, M · 2016
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Fast dictionary learning with a smoothed wasserstein loss
Rolet, A., Cuturi, M., and Peyré, G · 2016
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Entropic metric alignment for correspondence problems
Solomon, J., Peyré, G., Kim, V. G., and Sra, S · 2016
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Wasserstein generative adversarial networks
Arjovsky, M., Chintala, S., and Bottou, L · 2017
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Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance
Weed, J. and Bach, F · 2018
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Autoencoder and optimal transport to infer single-cell trajectories of biological processes
Yang, K. D., Damodaran, K., Venkatchalapathy, S., Soylemezoglu, A. C., Shivashankar, G., and Uhler, C · 2018
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Unsupervised hyper-alignment for multilingual word embeddings
Alaux, J., Grave, E., Cuturi, M., and Joulin, A · 2019
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Adversarial examples from computational constraints
Bubeck, S., Lee, Y. T., Price, E., and Razenshteyn, I. P · 2019
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del Barrio, E., Inouzhe, H., Loubes, J.-M., Matrán, C., and Mayo-Íscar, A · 2019
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Wasserstein regularization for sparse multi-task regression
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Generalized sliced Wasserstein distances
Kolouri, S., Nadjahi, K., Simsekli, U., Badeau, R., and Rohde, G. K · 2019
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Statistical inference for Bures-Wasserstein barycenters
Kroshnin, A., Spokoiny, V., and Suvorikova, A · 2019
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Fast convergence of empirical barycenters in Alexandrov spaces and the Wasserstein space
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Liang, T · 2019
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CycleGAN with a Blur Kernel for Deconvolution Microscopy: Optimal Transport Geometry
Lim, S., Lee, S.-E., Chang, S., and Ye, J. C · 2019
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Panaretos, V. M. and Zemel, Y · 2019
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Subspace robust Wasserstein distances
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Fréchet means and procrustes analysis in wasserstein space
Zemel, Y. and Panaretos, V. M · 2019
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