Maximin effects in inhomogeneous large-scale data

Annals of Statistics

Volumn 43, Issue 4, 2015, Pages 1801-1830

  Meinshausen, Nicolai ^a   Bühlmann, Peter ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Aggregation; Big data; Mixture models; Regularization; Robustness

Indexed keywords

EID: 84933565372     PISSN: 00905364     EISSN: 21688966     Source Type: Journal    
DOI: 10.1214/15-AOS1325     Document Type: Article

References (38)

1. AITKIN, M. and RUBIN, D. B. (1985). Estimation and hypothesis testing in finite mixture models. J. R. Stat. Soc. Ser. B. Stat. Methodol. 47 67-75.
2. AUDIBERT, J.-Y., BUBECK, S. and LUGOSI, G. (2014). Regret in online combinatorial optimization. Math. Oper. Res. 39 31-45. MR3173002
3. AUER, P., CESA-BIANCHI, N. and FISCHER, P. (2002). Finite-time analysis of the multiarmed bandit problem. Mach. Learn. 47 235-256.
4. BACH, F. R. (2008). Bolasso: Model consistent Lasso estimation through the bootstrap. In Proceedings of the 25th International Conference on Machine Learning 33-40. ACM, New York.
5. BARTLETT, P. L., DANI, V., HAYES, T., KAKADE, S., RAKHLIN, A. and TEWARI, A. (2008). High-probability regret bounds for bandit online linear optimization. Technical report, Univ. California, Berkeley, CA.
6. BRADIC, J. (2013). Efficient support recovery via weighted maximum-contrast subagging. Preprint. Available at arXiv:1306.3494.
7. BÜHLMANN, P. and VAN DE GEER, S. (2011). Statistics for High-Dimensional Data: Methods, Theory and Applications. Springer, Heidelberg. MR2807761
8. CAI, Z., FAN, J. and LI, R. (2000). Efficient estimation and inferences for varying-coefficient models. J. Amer. Statist. Assoc. 95 888-902. MR1804446
9. CARLSTEIN, E. G., MÜLLER, H. G. and SIEGMUND, D. (1994). Change-Point Problems. IMS, Hayward, CA. MR1477909
10. CESA-BIANCHI, N. and LUGOSI, G. (2006). Prediction, Learning, and Games. Cambridge Univ. Press, Cambridge. MR2409394
11. CHEN, S. S., DONOHO, D. L. and SAUNDERS, M. A. (2001). Atomic decomposition by basis pursuit. SIAM Rev. 43 129-159. MR1854649
12. DEMPSTER, A. P., LAIRD, N. M. and RUBIN, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. Ser. B. Stat. Methodol. 39 1-38. MR0501537
13. ELDAR, Y. C., BEN-TAL, A. and NEMIROVSKI, A. (2004). Linear minimax regret estimation of deterministic parameters with bounded data uncertainties. IEEE Trans. Signal Process. 52 2177-2188. MR2085579
14. FAN, J. and ZHANG, W. (1999). Statistical estimation in varying coefficient models. Ann. Statist. 27 1491-1518. MR1742497
15. FIGUEIREDO, M. A. T. and JAIN, A. K. (2002). Unsupervised learning of finite mixture models. IEEE Trans. Pattern Anal. Mach. Intell. 24 381-396.
16. FOSTER, D. P. and VOHRA, R. (1999). Regret in the on-line decision problem. Games Econom. Behav. 29 7-35. MR1729308
17. FRIEDMAN, J., HASTIE, T. and TIBSHIRANI, R. (2009). glmnet: Lasso and elastic-net regularized generalized linear models. R Package Version 1.
18. GENOVESE, C. R., JIN, J., WASSERMAN, L. and YAO, Z. (2012). A comparison of the lasso and marginal regression. J. Mach. Learn. Res. 13 2107-2143. MR2956354
19. HAMPEL, F. R., RONCHETTI, E. M., ROUSSEEUW, P. J. and STAHEL, W. A. (1986). Robust Statistics: The Approach Based on Influence Functions. Wiley, New York. MR0829458
20. HAND, D. J. (2006). Classifier technology and the illusion of progress. Statist. Sci. 21 1-34. MR2275965
21. HASTIE, T. and TIBSHIRANI, R. (1993). Varying-coefficient models. J. R. Stat. Soc. Ser. B. Stat. Methodol. 55 757-796. MR1229881
22. HOERL, A. E. and KENNARD, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics 12 55-67.
23. HUBER, P. J. (1964). Robust estimation of a location parameter. Ann. Math. Stat. 35 73-101. MR0161415
24. HUBER, P. J. (1973). Robust regression: Asymptotics, conjectures and Monte Carlo. Ann. Statist. 1 799-821. MR0356373
25. KOGAN, S., LEVIN, D., ROUTLEDGE, B. R., SAGI, J. S. and SMITH, N. A. (2009). Predicting risk from financial reports with regression. In Proceedings of Human Language Technologies: The 2009 Annual Conference of the North American Chapter of the Association for Computational Linguistics 272-280. ACM, New York.
26. KOLAR, M., SONG, L., AHMED, A. and XING, E. P. (2010). Estimating time-varying networks. Ann. Appl. Stat. 4 94-123. MR2758086
27. LAI, T. L. and ROBBINS, H. (1985). Asymptotically efficient adaptive allocation rules. Adv. in Appl. Math. 6 4-22. MR0776826
28. LECUÉ, G. and MENDELSON, S. (2015). Sparse recovery under weak moment assumptions. J. Eur. Math. Soc. To appear.
29. MCCULLOCH, C. E. (2006). Generalized Linear Mixed Models. Wiley, New York.
30. MCCULLOCH, C. E. and NEUHAUS, J. (2001). Generalized Linear Mixed Models. Wiley, New York.
31. MCLACHLAN, G. and PEEL, D. (2000). Finite Mixture Models. Wiley, New York. MR1789474
32. MEINSHAUSEN, N. and BÜHLMANN, P. (2010). Stability selection. J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 417-473. MR2758523
33. PINHEIRO, J. C. and BATES, D. M. (2000). Linear Mixed-Effects Models: Basic Concepts and Examples. Springer, Berlin.
34. RASKUTTI, G., WAINWRIGHT, M. J. and YU, B. (2010). Restricted eigenvalue properties for correlated Gaussian designs. J. Mach. Learn. Res. 11 2241-2259. MR2719855
35. 1-penalization for mixture regression models. TEST 19 209-256. MR2677722
36. TIBSHIRANI, R. (1996). Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B. Stat. Methodol. 58 267-288. MR1379242
37. WALD, A. (1945). Statistical decision functions which minimize the maximum risk. Ann. of Math. (2) 46 265-280. MR0012402
38. ZINKEVICH, M., JOHANSON, M., BOWLING, M. and PICCIONE, C. (2007). Regret minimization in games with incomplete information. In Advances in Neural Information Processing Systems 1729-1736. NIPS.