Competing against the best nearest neighbor filter in regression

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 6925 LNAI, Issue , 2011, Pages 129-143

  Dalalyan, Arnak S ^a,b   Salmon, Joseph ^a,b  

^a UNIVERSITÉ PARIS EST   (France)

^b Duke University   (United States)

Author keywords

adaptive smoothing; nonparametric regression; supervised learning

Indexed keywords

ADAPTIVE SMOOTHING; AGGREGATION STRATEGY; DESIGN STRATEGIES; LEARNING THEORY; NEAREST NEIGHBOR FILTERS; NEAREST-NEIGHBORS; NON-PARAMETRIC REGRESSION; THEORETICAL FRAMEWORK;

ALGORITHMS;

EID: 80054093390     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-24412-4_13     Document Type: Conference Paper

References (28)

1. Arlot, S., Bach, F.: Data-driven calibration of linear estimators with minimal penalties. In: NIPS, pp. 46-54 (2009)
2. Audibert, J.-Y.: Fast learning rates in statistical inference through aggregation. Ann. Statist. 37(4), 1591-1646 (2009)
3. Audibert, J.-Y., Tsybakov, A.B.: Fast learning rates for plug-in classifiers. Ann. Statist. 35(2), 608-633 (2007)
4. Baraud, Y., Giraud, C., Huet, S.: Estimator selection in the gaussian setting (2010) (submitted)
5. Ben-David,S.,Pal,D.,Shalev-Shwartz,S.:Agnosticonline learning. In:COLT(2009)
6. Breiman, L.: Better subset regression using the nonnegative garrote. Technometrics 37, 373-384 (1995)
7. Buckheit, J.B., Donoho, D.L.: Wavelab and reproducible research. In: Wavelets and Statistics. Lect. Notes Statist., vol. 103, pp. 55-81. Springer, New York (1995)
8. Catoni, O.: Statistical learning theory and stochastic optimization. Lecture Notes in Mathematics, vol. 1851. Springer, Berlin (2004)
9. Cesa-Bianchi, N., Lugosi, G.: Prediction, learning, and games. Cambridge University Press, Cambridge (2006)
10. Cesa-Bianchi, N., Mansour, Y., Stoltz, G.: Improved second-order bounds for prediction with expert advice. Mach. Learn. 66, 321-352 (2007)
11. Cornillon, P.-A., Hengartner, N., Matzner-Løber, E.: Recursive bias estimation for multivariate regression smoothers (2009) (submitted)
12. Dalalyan, A.S., Salmon, J.: Sharp oracle inequalities for aggregation of affine estimators. technical report, arXiv:1104.3969v2 [math.ST] (2011)
13. Dalalyan, A.S., Tsybakov, A.B.: Aggregation by exponential weighting, sharp pacbayesian bounds and sparsity. Mach. Learn. 72(1-2), 39-61 (2008)
14. Dalalyan, A.S., Tsybakov, A.B.: Sparse regression learning by aggregation and Langevin Monte-Carlo. In: COLT (2009)
15. Devroye, L., Györfi, L., Lugosi, G.: A probabilistic theory of pattern recognition. Applications of Mathematics, vol. 31. Springer, New York (1996)
16. George, E.I.: Minimax multiple shrinkage estimation. Ann. Statist. 14(1), 188-205 (1986)
17. Gerchinovitz, S.: Sparsity regret bounds for individual sequences in online linear regression (submitted, 2011)
18. Goldenshluger, A., Lepski, O.V.: Universal pointwise selection rule in multivariate function estimation. Bernoulli 14(4), 1150-1190 (2008)
19. Kalai, A., Klivans, A., Mansour, Y., Servedio, R.: Agnostically learning halfspaces. SIAM J. Comput. 37(6), 1777-1805 (2008)
20. Kearns, M.J., Schapire, R.E., Sellie, L.: Toward efficient agnostic learning. Machine Learning 17(2-3), 115-141 (1994)
21. Kivinen, J., Warmuth, M.K.: Averaging expert predictions. In: Fischer, P., Simon, H.U. (eds.) EuroCOLT 1999. LNCS (LNAI), vol. 1572, pp. 153-167. Springer, Heidelberg (1999)
22. Lafferty, J., Wasserman, L.: Rodeo: sparse, greedy nonparametric regression. Ann. Statist. 36(1), 28-63 (2008)
23. Lepski, O.V., Mammen, E., Spokoiny, V.G.: Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors. Ann. Statist. 25(3), 929-947 (1997)
24. Leung, G., Barron, A.R.: Information theory and mixing least-squares regressions. IEEE Trans. Inf. Theory 52(8), 3396-3410 (2006)
25. Li, K.-C.: From Stein's unbiased risk estimates to the method of generalized cross validation. Ann. Statist. 13(4), 1352-1377 (1985)
26. Salmon, J., Dalalyan, A.S.: Optimal aggregation of affine estimators. In: COLT (2011)
27. Stein, C.M.: Estimation of the mean of a multivariate distribution. In: Proc. Prague Symp. Asymptotic Statist (1973)
28. Tsybakov, A.B.: Optimal rates of aggregation. In: COLT, pp. 303-313 (2003)