EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 23 (2019) ESAIM: PS, 23 (2019) 841-873 References
Open Access
Issue
ESAIM: PS
Volume 23, 2019
Page(s) 841 - 873
DOI https://doi.org/10.1051/ps/2019011
Published online 24 December 2019
  1. F. Bach, Adaptivity of averaged stochastic gradient descent to local strong convexity for logistic regression. J. Mach. Learn. Res. 15 (2014) 595–627. [Google Scholar]
  2. Borwein and P.B. Borwein, Pi and the AGM. Wiley, New York (1987). [Google Scholar]
  3. S. Boyd and L. Vandenberghe, Convex optimization. Cambridge University Press (2004). [Google Scholar]
  4. H. Cardot and A. Godichon-Baggioni, Fast estimation of the median covariation matrix with application to online robust principal components analysis. TEST 26 (2017) 461–480. [CrossRef] [Google Scholar]
  5. H. Cardot, P. Cénac and P.-A. Zitt, Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm. Bernoulli 19 (2013) 18–43. [CrossRef] [Google Scholar]
  6. H. Cardot, P. Cénac, A. Godichon-Baggioni et al., Online estimation of the geometric median in hilbert spaces: non asymptotic confidence balls. Ann. Stat. 45 (2017) 591–614. [Google Scholar]
  7. P. Chaudhuri, Multivariate location estimation using extension of R-estimates through U-statistics type approach. Ann. Statist. 20 (1992) 897–916. [CrossRef] [Google Scholar]
  8. P. Chaudhuri, On a geometric notion of quantiles for multivariate data. J. Am. Stat. Assoc. 91 (1996) 862–872. [Google Scholar]
  9. Y. Chen, X. Dang, H. Peng and H.L. Bart, Outlier detection with the kernelized spatial depth function. IEEE Trans. Pattern Anal. Mach. Intel. 31 (2009) 288–305. [Google Scholar]
  10. Cohen, A. Nedic and R. Srikant, On projected stochastic gradient descent algorithm with weighted averaging for least squares regression. In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2016) 2314–2318. [CrossRef] [Google Scholar]
  11. M. Duflo, Algorithmes stochastiques. Springer, Berlin (1996). [Google Scholar]
  12. Duflo, Random iterative models, Vol. 34 of Applications of Mathematics (New York). Translated fromthe 1990 French original by Stephen S. Wilson and revised by the author. Springer-Verlag, Berlin (1997). [Google Scholar]
  13. S. Ghadimi and G. Lan, Optimal stochastic approximation algorithms for strongly convex stochastic composite optimization I: a generic algorithmic framework. SIAM J. Optim. 22 (2012) 1469–1492. [Google Scholar]
  14. A. Godichon-Baggioni, Estimating the geometric median in hilbert spaces with stochastic gradient algorithms: Lp and almost sure rates of convergence. J. Multivar. Anal. 146 (2016) 209–222. [Google Scholar]
  15. A. Goh, C. Lenglet, P.M. Thompson and R. Vidal, A nonparametric Riemannian framework for processing high angular resolution diffusion images (HARDI). IEEE Conference on Computer Vision and Pattern Recognition (2009) 2496–2503. [Google Scholar]
  16. J.B.S. Haldane, Note on the median of a multivariate distribution. Biometrika 35 (1948) 414–417. [Google Scholar]
  17. M. Hallin and D. Paindaveine, Semiparametrically efficient rank-based inference for shape. I. Optimal rank-based tests for sphericity. Ann. Stat. 34 (2006) 2707–2756. [Google Scholar]
  18. P. Huber and E. Ronchetti, Robust Statistics, 2nd edn. John Wiley and Sons (2009). [CrossRef] [Google Scholar]
  19. J. Kemperman, The median of a finite measure on a Banach space. In Statistical data analysis based on the L1 -norm and related methods (Neuchâtel, 1987). North-Holland, Amsterdam (1987) 217–230. [Google Scholar]
  20. H.J. Kushner and G.G. Yin, Stochastic approximation and recursive algorithms and applications, Stochastic Modelling and Applied Probability. 2nd edn. Vol. 35 of Applications of Mathematics (New York). Springer-Verlag, New York (2003). [Google Scholar]
  21. R.A. Maronna, R.D. Martin and V.J. Yohai, Robust statistics. Theory and methods. Wiley Series in Probability and Statistics. John Wiley& Sons, Ltd., Chichester (2006). [CrossRef] [Google Scholar]
  22. E. Moulines and F.R. Bach, Non-asymptotic analysis of stochastic approximation algorithms for machine learning. In Advances in Neural Information Processing Systems (2011) 451–459. [Google Scholar]
  23. M. Pelletier, On the almost sure asymptotic behaviour of stochastic algorithms. Stoch. Process. Appl. 78 (1998) 217–244. [CrossRef] [MathSciNet] [Google Scholar]
  24. M. Pelletier, Asymptotic almost sure efficiency of averaged stochastic algorithms. SIAM J. Control Optim. 39 (2000) 49–72. [Google Scholar]
  25. G.H. Polya, G. Harold and Littlewood, Inequalities. University Press (1952). [Google Scholar]
  26. B. Polyak and A. Juditsky, Acceleration of stochastic approximation. SIAM J. Cont. Optim. 30 (1992) 838–855. [CrossRef] [MathSciNet] [Google Scholar]
  27. H. Robbins and S. Monro, A stochastic approximation method. Ann. Math. Stat. (1951) 400–407. [CrossRef] [MathSciNet] [Google Scholar]
  28. M. Rudelson, Recent developments in non-asymptotic theory of random matrices. Modern Aspects of Random Matrix Theory. In Vol. 72 of Proceedings of Symposia in Applied Mathematics (2014) 83–120. [CrossRef] [Google Scholar]
  29. D. Ruppert, Efficient estimations from a slowly convergent robbins-monro process. Technical report, Cornell University Operations Research and Industrial Engineering (1988). [Google Scholar]
  30. R. Serfling, Depth functions in nonparametric multivariate inference. In Vol. 72 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science 72 (2006). [Google Scholar]
  31. P. Turaga, A. Veeraraghavan and R. Chellappa, Statistical analysis on Stiefel and Grassmann manifolds with applications in computer vision. IEEE Conference on Computer Vision and Pattern Recognition (2008). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.