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Projection robust Wasserstein (PRW) distance, or Wasserstein projection pursuit (WPP), is a robust variant of the Wasserstein distance.
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Topics in Optimal Transportation , volume 58
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Optimal Transport: Old and New , volume 338
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Optimization Algorithms on Matrix Manifolds
P-A. Absil, R. Mahony, and R. Sepulchre · 2009
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On complexity of finding stationary points of nonsmooth nonconvex functions
J. Zhang, H. Lin, S. Sra, and A. Jadbabaie · 2009
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Displacement interpolation using lagrangian mass transport
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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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Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
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A feasible method for optimization with orthogonality constraints
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Fast computation of Wasserstein barycenters
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Iteration complexity of feasible descent methods for convex optimization
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Sliced and radon Wasserstein barycenters of measures
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On the rate of convergence in Wasserstein distance of the empirical measure
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Convex Analysis , volume 36
R. T. Rockafellar · 2015
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WASP: Scalable Bayes via barycenters of subset posteriors
S. Srivastava, V. Cevher, Q. Dinh, and D. Dunson · 2015
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Convergence rates of parameter estimation for some weakly identifiable finite mixtures
N. Ho and L. Nguyen · 2016
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Fast dictionary learning with a smoothed Wasserstein loss
A. Rolet, M. Cuturi, and G. Peyré · 2016
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First-order methods for geodesically convex optimization
H. Zhang and S. Sra · 2016
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A collection of nonsmooth Riemannian optimization problems
P-A. Absil and S. Hosseini · 2019
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Riemannian adaptive optimization methods
G. Becigneul and O-E. Ganea · 2019
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Global rates of convergence for nonconvex optimization on manifolds
N. Boumal, P-A. Absil, and C. Cartis · 2019
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Efficiently escaping saddle points on manifolds
C. Criscitiello and N. Boumal · 2019
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User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient
A. S. Dalalyan and A. Karagulyan · 2019
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Stochastic model-based minimization of weakly convex functions
D. Davis and D. Drusvyatskiy · 2019
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Riemannian SVRG: Fast stochastic optimization on Riemannian manifolds
H. Zhang, S. J. Reddi, and S. Sra · 2016
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Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration
J. Altschuler, J. Niles-Weed, and P. Rigollet · 2017
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Wasserstein generative adversarial networks
M. Arjovsky, S. Chintala, and L. Bottou · 2017
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A distributional perspective on reinforcement learning
M. G. Bellemare, W. Dabney, and R. Munos · 2017
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Iteration-complexity of gradient, subgradient and proximal point methods on Riemannian manifolds
G. C. Bento, O. P. Ferreira, and J. G. Melo · 2017
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Optimal transport for domain adaptation
N. Courty, R. Flamary, D. Tuia, and A. Rakotomamonjy · 2017
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Statistical optimal transport via factored couplings
A. Forrow, J-C. Hütter, M. Nitzan, P. Rigollet, G. Schiebinger, and J. Weed · 2019
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Sample complexity of Sinkhorn divergences
A. Genevay, L. Chizat, F. Bach, M. Cuturi, and G. Peyré · 2019
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Accelerated alternating minimization, accelerated Sinkhorn’s algorithm and accelerated iterative Bregman projections
S. Guminov, P. Dvurechensky, N. Tupitsa, and A. Gasnikov · 2019
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Structured quasi-Newton methods for optimization with orthogonality constraints
J. Hu, B. Jiang, L. Lin, Z. Wen, and Y. Yuan · 2019
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Riemannian adaptive stochastic gradient algorithms on matrix manifolds
H. Kasai, P. Jawanpuria, and B. Mishra · 2019
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Generalized sliced Wasserstein distances
S. Kolouri, K. Nadjahi, U. Simsekli, R. Badeau, and G. Rohde · 2019
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Nonsmooth optimization over Stiefel manifold: Riemannian subgradient methods
X. Li, S. Chen, Z. Deng, Q. Qu, Z. Zhu, and A. M-C. So · 2019
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Quadratic optimization with orthogonality constraint: explicit łojasiewicz exponent and linear convergence of retraction-based line-search and stochastic variance-reduced gradient methods
H. Liu, A. M-C. So, and W. Wu · 2019
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Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem
G. Mena and J. Niles-Weed · 2019
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High-order Langevin diffusion yields an accelerated MCMC algorithm
W. Mou, Y-A. Ma, M. J. Wainwright, P. L. Bartlett, and M. I. Jordan · 2019
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SGD without replacement: sharper rates for general smooth convex functions
D. Nagaraj, P. Jain, and P. Netrapalli · 2019
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Estimation of Wasserstein distances in the spiked transport model
J. Niles-Weed and P. Rigollet · 2019
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Subspace robust Wasserstein distances
F-P. Paty and M. Cuturi · 2019
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Computational optimal transport
G. Peyré and M. Cuturi · 2019
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Optimal-transport analysis of single-cell gene expression identifies developmental trajectories in reprogramming
G. Schiebinger, J. Shu, M. Tabaka, B. Cleary, V. Subramanian, A. Solomon, J. Gould, S. Liu, S. Lin, and P. Berube · 2019
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Escaping from saddle points on Riemannian manifolds
Y. Sun, N. Flammarion, and M. Fazel · 2019
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Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance
J. Weed and F. Bach · 2019
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Primal-dual optimization algorithms over Riemannian manifolds: an iteration complexity analysis
J. Zhang, S. Ma, and S. Zhang · 2019
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Proximal gradient method for nonsmooth optimization over the Stiefel manifold
S. Chen, S. Ma, A. M-C. So, and T. Zhang · 2020
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Multi-subject MEG/EEG source imaging with sparse multi-task regression
H. Janati, T. Bazeille, B. Thirion, M. Cuturi, and A. Gramfort · 2020
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Convergence and concentration of empirical measures under Wasserstein distance in unbounded functional spaces
J. Lei · 2020
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Distributional sliced-Wasserstein and applications to generative modeling
K. Nguyen, N. Ho, T. Pham, and H. Bui · 2020
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Can we find near-approximately-stationary points of nonsmooth nonconvex functions?
O. Shamir · 2020
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Predicting cell lineages using autoencoders and optimal transport
K. D. Yang, K. Damodaran, S. Venkatachalapathy, A. Soylemezoglu, G. V. Shivashankar, and C. Uhler · 2020
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On projection robust optimal transport: Sample complexity and model misspecification
T. Lin, Z. Zheng, E. Y. Chen, M. Cuturi, and M. I. Jordan · 2021
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