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All issues Volume 26 (2022) ESAIM: PS, 26 (2022) 436-472 References
Open Access
Issue
ESAIM: PS
Volume 26, 2022
Page(s) 436 - 472
DOI https://doi.org/10.1051/ps/2022015
Published online 08 December 2022
  1. M. Agueh and G. Carlier, Barycenters in the Wasserstein space. SIAM J. Math. Anal. 43 (2011) 904–924. [Google Scholar]
  2. J. Alschuler and E. Boix-Adsera, Wasserstein barycenters are NP-hard to compute. Preprint [arXiv:2101.01100] (2021). [Google Scholar]
  3. P.C. Alvarez-Esteban, E. del Barrio, J.A. Cuesta-Albertos and C. Matrán, A fixed-point approach to barycenters in Wasserstein space. J. Math. Anal. Appi. 441 (2016) 744–762. [Google Scholar]
  4. P.C. Lvarez-Esteban, E. del Barrio, J.A. Cuesta-Albertos and C. Matráan, Wide Consensus aggregation in the Wasserstein Space. Application to location-scatter families. Bernoulli 24 (2018) 3147–3179. [MathSciNet] [Google Scholar]
  5. L. Ambrosio, N. Gigli and G. Savará, Gradient flows in metric spaces and in the space of probability measures. Lectures in Mathematics ETH Zurich, 2nd edn., Birkhäuser Verlag, Basel (2008). [Google Scholar]
  6. C. Andrieu, N. De Freitas, A. Doucet and M.I. Jordan, An introduction to MCMC for machine learning. Mach. Learn. 50 (2003) 5–43. [Google Scholar]
  7. J. Backhoff-Veraguas, J. Fontbona, G. Rios and F. Tobar, Stochastic gradient descent in Wasserstein space. Preprint [arXiv:2201.04232] (2022). [Google Scholar]
  8. J.O. Berger, Statistical decision theory and Bayesian analysis. Springer Science & Business Media (2013). [Google Scholar]
  9. R.H. Berk et al., Limiting behavior of posterior distributions when the model is incorrect. Ann. Math. Stat. 37 (1966) 51–58. [CrossRef] [Google Scholar]
  10. J. Bigot and T. Klein, Characterization of barycenters in the Wasserstein space by averaging optimal transport maps. ESAIM: Probab. Stat. 22 (2018) 35–57. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  11. S. Brooks, A. Gelman, G. Jones and X.-L. Meng, Handbook of Markov chain Monte Carlo. CRC Press (2011). [Google Scholar]
  12. E. Cazelles, F. Tobar and J. Fontbona, A novel notion of barycenter for probability distributions based on optimal weak mass transport, 2021 Conference on Neural Information Processing Systems NeurIPS (2021) [arXiv:2102.13380]. [Google Scholar]
  13. S. Chewi, T. Maunu, P. Rigollet and A.J. Stromme, Gradient descent algorithms for Bures-Wasserstein barycenters, in Conference on Learning Theory, PMLR (2020) 1276–1304. [Google Scholar]
  14. J. Cuesta-Albertos, L. Ruschendorf and A. Tuero-Diaz, Optimal coupling of multivariate distributions and stochastic processes. J. Multivariate Anal. 46 (1993) 335–361. [Google Scholar]
  15. M. Cuturi and A. Doucet, Fast computation of Wasserstein barycenters, in International Conference on Machine Learning (2014) 685–693. [Google Scholar]
  16. M. Cuturi and G. Peyrá, A smoothed dual approach for variational Wasserstein problems. SIAM J. Imag. Sci. 9 (2016) 320–343. [Google Scholar]
  17. P. Diaconis and D. Freedman, On the consistency of Bayes estimates. Ann. Stat. (1986) 1–26. [Google Scholar]
  18. P. Dognin, I. Melnyk, Y. Mroueh, J. Ross, C.D. Santos and T. Sercu, Wasserstein barycenter model ensembling. Preprint [arXiv:1902.04999] (2019). [Google Scholar]
  19. D.C. Dowson and B.V. Landau, The Frechet distance between multivariate normal distributions. J. Multivariate Anal. 12 (1982) 450–455. [Google Scholar]
  20. T.A. El Moselhy and Y.M. Marzouk, Bayesian inference with optimal maps. J. Comput. Phys. 231 (2012) 7815–7850. [CrossRef] [MathSciNet] [Google Scholar]
  21. R. Flamary and N. Courty, POT Python Optimal Transport library (2017). [Google Scholar]
  22. M. Fráchet, Les áláments aláatoires de nature quelconque dans un espace distanciá, in Annales de l’institut Henri Poincará 10 (1948) 215–310. [Google Scholar]
  23. S. Ghosal and A. van der Vaart, vol. 44 of Fundamentals of nonparametric Bayesian inference. Cambridge University Press (2017). [Google Scholar]
  24. C.R. Givens and R.M. Shortt, A class of Wasserstein metrics for probability distributions. Michigan Math. J. 31 (1984) 231–240. [Google Scholar]
  25. J. Goodman and J. Weare, Ensemble samplers with affine invariance. Commun. Appl. Math. Comput. Sci. 5 (2010) 65–80. [CrossRef] [MathSciNet] [Google Scholar]
  26. M. Grendár and G. Judge, Asymptotic equivalence of empirical likelihood and Bayesian map. Ann. Statist. 37 (2009) 2445–2457. [CrossRef] [MathSciNet] [Google Scholar]
  27. S. Kim, D. Mesa, R. Ma and T.P. Coleman, Tractable fully Bayesian inference via convex optimization and optimal transport theory. Preprint [arXiv:1509.08582] (2015). [Google Scholar]
  28. Y.-H. Kim and B. Pass, Wasserstein barycenters over Riemannian manifolds. Adv. Math. 307 (2017) 640–683. [CrossRef] [MathSciNet] [Google Scholar]
  29. B.J.K. Kleijn, Bayesian asymptotics under misspecification, Ph.D. thesis, Vrije Universiteit Amsterdam (2004). [Google Scholar]
  30. B.J.K. Kleijn and A.W. Van der Vaart, The Bernstein-von-Mises theorem under misspecification. Electr. J. Stat. 6 (2012) 354–381. [Google Scholar]
  31. A. Korotin, V. Egiazarian, L. Lingxiao and E. Burnaev, Wasserstein Iterative Networks for Barycenter Estimation. [arXiv:2201.12245] (2022). [Google Scholar]
  32. J. Lacombe, J. Digne, N. Courty and N. Bonneel, Learning to generate Wasserstein barycenters. Preprint [arXiv:2102.12178] (2021). [Google Scholar]
  33. T. Le Gouic and J.-M. Loubes, Existence and consistency of Wasserstein Barycenters. Probab. Theory Related Fields 168 (2017) 901–917. [Google Scholar]
  34. A. Mallasto, A. Gerolin and H.Q. Minh, Entropy-regularized 2-Wasserstein distance between Gaussian measures. Inf. Geometry (2021) 1–35. [Google Scholar]
  35. Y. Marzouk, T. Moselhy, M. Parno and A. Spantini, Sampling via measure transport: An introduction. Handbook of Uncertainty Quantification (2016) 1–41. [Google Scholar]
  36. P. Massart, Concentration Inequalities and Model Selection. Springer (2007). [Google Scholar]
  37. K.P. Murphy, Machine learning: a probabilistic perspective. The MIT Press, Cambridge, MA (2012). [Google Scholar]
  38. V.M. Panaretos and Y. Zemel, An invitation to statistics in Wasserstein space. SpringerBriefs in Probability and Mathematical Statistics, Springer, Cham (2020). [Google Scholar]
  39. M. Parno, Transport maps for accelerated Bayesian computation, Ph.D. thesis, Massachusetts Institute of Technology (2015). [Google Scholar]
  40. B. Pass, Optimal transportation with infinitely many marginals. J. Funct. Anal. 264 (2013) 947–963. [CrossRef] [MathSciNet] [Google Scholar]
  41. G. Peyré and M. Cuturi, Computational optimal transport: with applications to data science. Found. Trends Mach. Learn. 11 (2019) 355–607. [CrossRef] [Google Scholar]
  42. H. Robbins and S. Monro, A stochastic approximation method. Ann. Math. Stat. (1951) 400–407. [CrossRef] [Google Scholar]
  43. F. Santambrogio, Optimal transport for applied mathematicians. Birkauser, NY (2015) 99–102. [Google Scholar]
  44. L. Schwartz, On Bayes procedures. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 4 (1965) 10–26. [Google Scholar]
  45. C. Villani, Topics in optimal transportation. Graduate Studies in Mathematics, vol. 58, American Mathematical Society, Providence, RI (2003). [CrossRef] [Google Scholar]
  46. C. Villani, Optimal transport. Old and new, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 338. Springer-Verlag, Berlin (2009). [CrossRef] [Google Scholar]
  47. R. Wang, X. Wang and L. Wu, Sanov’s theorem in the Wasserstein distance: a necessary and sufficient condition. Stat. Probab. Lett. 80 (2010) 505–512. [Google Scholar]
  48. Y. Zemel and V. Panaretos, Fréchet means and Procrustes analysis in Wasserstein space. Bernoulli 25 (2019) 932–976. [CrossRef] [MathSciNet] [Google Scholar]

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