Fetching the paper…
Reading the bibliography…
In the machine learning and optimization community, there are two main approaches for the convex risk minimization problem, namely, the Stochastic Approximation (SA) and the Sample Average Approximation (SAA).
1901
Earlier work this paper cites.
1902
Earlier work this paper cites.
M. Fréchet, Les éléments aléatoires de nature quelconque dans un espace distancié , in Annales de l’institut Henri Poincaré , Vol. 10. 1948, pp. 215–310
1948
Earlier work this paper cites.
H. Robbins and S. Monro, A stochastic approximation method , The annals of mathematical statistics (1951), pp. 400–407
1951
Earlier work this paper cites.
1971
Earlier work this paper cites.
J. Franklin and J. Lorenz, On the scaling of multidimensional matrices , Linear Algebra and its Applications 114 (1989), pp. 717 – 735. Available at http://www.sciencedirect.com/science/article/pii/0024379589904904 , Special Issue Dedicated to Alan J. Hoffman
1989
Earlier work this paper cites.
H.N. Gabow and R.E. Tarjan, Faster scaling algorithms for general graph matching problems , Journal of the ACM (JACM) 38 (1991), pp. 815–853
1991
Earlier work this paper cites.
R.K. Ahuja, T.L. Magnanti, and J.B. Orlin, Network flows: Theory , Algorithms, and Applications 526 (1993)
1993
Earlier work this paper cites.
Y. Rubner, C. Tomasi, and L.J. Guibas, A metric for distributions with applications to image databases , in Sixth International Conference on Computer Vision (IEEE Cat. No. 98CH36271) . IEEE, 1998, pp. 59–66
1998
Earlier work this paper cites.
A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization. , Society for Industrial and Applied Mathematics, 2001, Available at http://epubs.siam.org/doi/abs/10.1137/1.9780898718829
2001
Earlier work this paper cites.
2001
Earlier work this paper cites.
Y. Nesterov, Primal-dual subgradient methods for convex problems , Mathematical Programming 120 (2009), pp. 221–259. Available at https://doi.org/10.1007/s10107-007-0149-x , First appeared in 2005 as CORE discussion paper 2005/67
2005
Earlier work this paper cites.
A. Shapiro and A. Nemirovski, On complexity of stochastic programming problems , in Continuous optimization , Springer, 2005, pp. 111–146
2005
Earlier work this paper cites.
J. Duchi, S. Shalev-Shwartz, Y. Singer, and T. Chandra, Efficient projections onto the l 1-ball for learning in high dimensions , in Proceedings of the 25th international conference on Machine learning . 2008, pp. 272–279
2008
Earlier work this paper cites.
A. Juditsky, P. Rigollet, A.B. Tsybakov, et al. , Learning by mirror averaging , The Annals of Statistics 36 (2008), pp. 2183–2206
2008
Earlier work this paper cites.
S.M. Kakade and A. Tewari, On the generalization ability of online strongly convex programming algorithms , in Advances in Neural Information Processing Systems . 2009, pp. 801–808
2009
Earlier work this paper cites.
A. Nemirovski, A. Juditsky, G. Lan, and A. Shapiro, Robust stochastic approximation approach to stochastic programming , SIAM Journal on Optimization 19 (2009), pp. 1574–1609. Available at https://doi.org/10.1137/070704277
2009
Earlier work this paper cites.
S. Shalev-Shwartz, O. Shamir, N. Srebro, and K. Sridharan, Stochastic Convex Optimization. , in COLT . 2009
2009
Earlier work this paper cites.
A. Shapiro, D. Dentcheva, and A. Ruszczyński, Lectures on Stochastic Programming , Society for Industrial and Applied Mathematics, 2009, Available at http://epubs.siam.org/doi/abs/10.1137/1.9780898718751
2009
Earlier work this paper cites.
W. Wang, J.A. Ozolek, D. Slepcev, A.B. Lee, C. Chen, and G.K. Rohde, An optimal transportation approach for nuclear structure-based pathology , IEEE transactions on medical imaging 30 (2010), pp. 621–631
2010
Earlier work this paper cites.
M. Agueh and G. Carlier, Barycenters in the wasserstein space , SIAM Journal on Mathematical Analysis 43 (2011), pp. 904–924
2011
Earlier work this paper cites.
J. Rabin, G. Peyré, J. Delon, and M. Bernot, Wasserstein barycenter and its application to texture mixing , in International Conference on Scale Space and Variational Methods in Computer Vision . Springer, 2011, pp. 435–446
2011
Earlier work this paper cites.
S.T. Rachev, S.V. Stoyanov, and F.J. Fabozzi, A probability metrics approach to financial risk measures , John Wiley & Sons, 2011
2011
Earlier work this paper cites.
2012
Earlier work this paper cites.
J. Bigot, T. Klein, et al. , Consistent estimation of a population barycenter in the Wasserstein space , ArXiv e-prints (2012)
2012
Earlier work this paper cites.
A. Juditsky and A. Nemirovski, First order methods for non-smooth convex large-scale optimization, i: General purpose methods , in Optimization for Machine Learning , S.W. Suvrit Sra Sebastian Nowozin, ed., Cambridge, MA: MIT Press, 2012, pp. 121–184
2012
Earlier work this paper cites.
V. Spokoiny, et al. , Parametric estimation. finite sample theory , The Annals of Statistics 40 (2012), pp. 2877–2909
2012
Cited alongside, same era.
M. Cuturi, Sinkhorn distances: Lightspeed computation of optimal transport , in Advances in Neural Information Processing Systems 26 , C.J.C. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K.Q. Weinberger, eds., Curran Associates, Inc., 2013, pp. 2292–2300. Available at http://papers.nips.cc/paper/4927-sinkhorn-distances-lightspeed-computation-of-optimal-transport.pdf
2013
Cited alongside, same era.
Y.T. Lee and A. Sidford, Path Finding Methods for Linear Programming: Solving Linear Programs in O ~ ( rank ) \tilde{O}(\sqrt{\text{rank}}) Iterations and Faster Algorithms for Maximum Flow , in 2014 IEEE 55th Annual Symposium on Foundations of Computer Science , Oct. 2014, pp. 424–433
2014
Cited alongside, same era.
S. Shalev-Shwartz and S. Ben-David, Understanding machine learning: From theory to algorithms , Cambridge university press, 2014
M. Sommerfeld and A. Munk, Inference for empirical Wasserstein distances on finite spaces , Journal of the Royal Statistical Society: Series B (Statistical Methodology) 80 (2018), p. 219–238
2018
Later among the works it cites.
J. Bigot, E. Cazelles, and N. Papadakis, Central limit theorems for entropy-regularized optimal transport on finite spaces and statistical applications (2019)
2019
Later among the works it cites.
J. Bigot, E. Cazelles, and N. Papadakis, Data-driven regularization of wasserstein barycenters with an application to multivariate density registration , Information and Inference: A Journal of the IMA 8 (2019), pp. 719–755
2019
Later among the works it cites.
J. Bigot, E. Cazelles, and N. Papadakis, Penalization of barycenters in the Wasserstein space , SIAM Journal on Mathematical Analysis 51 (2019), pp. 2261–2285
2019
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2014
Cited alongside, same era.
J.D. Benamou, G. Carlier, M. Cuturi, L. Nenna, and G. Peyré, Iterative bregman projections for regularized transportation problems , SIAM Journal on Scientific Computing 37 (2015), pp. A1111–A1138
2015
Cited alongside, same era.
E. Boissard, T. Le Gouic, J.M. Loubes, et al. , Distribution’s template estimate with wasserstein metrics , Bernoulli 21 (2015), pp. 740–759
2015
Cited alongside, same era.
2015
Cited alongside, same era.
A. Gramfort, G. Peyré, and M. Cuturi, Fast optimal transport averaging of neuroimaging data , in International Conference on Information Processing in Medical Imaging . Springer, 2015, pp. 261–272
2015
Cited alongside, same era.
M. Kusner, Y. Sun, N. Kolkin, and K. Weinberger, From word embeddings to document distances , in International conference on machine learning . PMLR, 2015, pp. 957–966
2015
Cited alongside, same era.
J. Rabin and N. Papadakis, Convex color image segmentation with optimal transport distances , in International Conference on Scale Space and Variational Methods in Computer Vision . Springer, 2015, pp. 256–269
2015
Cited alongside, same era.
J. Solomon, F. De Goes, G. Peyré, M. Cuturi, A. Butscher, A. Nguyen, T. Du, and L. Guibas, Convolutional wasserstein distances: Efficient optimal transportation on geometric domains , ACM Transactions on Graphics (TOG) 34 (2015), p. 66
2015
Cited alongside, same era.
S. Srivastava, V. Cevher, Q. Dinh, and D. Dunson, WASP: Scalable Bayes via barycenters of subset posteriors , in Artificial Intelligence and Statistics . PMLR, 2015, pp. 912–920
2015
Cited alongside, same era.
E. Del Barrio, J.A. Cuesta-Albertos, C. Matrán, and A. Mayo-Íscar, Robust clustering tools based on optimal transportation , Statistics and Computing 29 (2019), pp. 139–160
2019
Later among the works it cites.
2019
Later among the works it cites.
2019
Later among the works it cites.
2019
Later among the works it cites.
2019
Later among the works it cites.
E. Hazan, et al. , Introduction to online convex optimization , Foundations and Trends® in Optimization 2 (2019), pp. 157–325
2019
Later among the works it cites.
A. Jambulapati, A. Sidford, and K. Tian, A direct O ~ ( 1 / ε ) \tilde{O}(1/\varepsilon) iteration parallel algorithm for optimal transport , in Advances in Neural Information Processing Systems . 2019, pp. 11359–11370
2019
Later among the works it cites.
2019
Later among the works it cites.
2019
Later among the works it cites.
F. Orabona, A modern introduction to online learning , arXiv preprint arXiv:1912.13213 (2019)
2019
Later among the works it cites.
V.M. Panaretos and Y. Zemel, Statistical aspects of wasserstein distances , Annual review of statistics and its application 6 (2019), pp. 405–431
2019
Later among the works it cites.
G. Peyré, M. Cuturi, et al. , Computational optimal transport , Foundations and Trends® in Machine Learning 11 (2019), pp. 355–607
2019
Later among the works it cites.
2020
Closest in time.
2020
Closest in time.
J. Delon and A. Desolneux, A Wasserstein-type distance in the space of Gaussian mixture models , SIAM Journal on Imaging Sciences 13 (2020), pp. 936–970
2020
Closest in time.
2020
Closest in time.
2020
Closest in time.
M. Klatt, C. Tameling, and A. Munk, Empirical regularized optimal transport: Statistical theory and applications , SIAM Journal on Mathematics of Data Science 2 (2020), pp. 419–443
2020
Closest in time.
G. Carlier, On the linear convergence of the multi-marginal sinkhorn algorithm (2021)
2021
Closest in time.
2021
Closest in time.
2034
Closest in time.
C. Frogner, C. Zhang, H. Mobahi, M. Araya, and T.A. Poggio, Learning with a Wasserstein loss , in Advances in Neural Information Processing Systems . 2015, pp. 2053–2061
2061
Closest in time.