Statistical and algorithmic perspectives on randomized sketching for ordinary least-squares

32nd International Conference on Machine Learning, ICML 2015

Volumn 1, Issue , 2015, Pages 617-625

  Raskutti, Garvesh ^a   Mahoney, Michael W ^b  

^a University of Wisconsin Madison   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; EFFICIENCY; ERRORS; LEARNING ALGORITHMS; LEARNING SYSTEMS; MEAN SQUARE ERROR; SAMPLING; STATISTICS;

ALGORITHMIC ASPECTS; LINEAR MODELING; MEAN SQUARED ERROR; NUMBER OF SAMPLES; ORDINARY LEAST SQUARES; ORIGINAL SAMPLE; RANDOM PROJECTIONS; STATISTICAL PREDICTION;

ALGORITHMS;

EID: 84969533825     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (21)

1. Avron, H., Maymounkov, P., and Toledo, S. Blendenpik: Supercharging LAPACK's least-squares solver. SIAM Journal on Scientific Computing, 32:1217-1236, 2010.
2. Boutsidis, C. and Gittens, A. Improved matrix algorithms via the subsampled randomized Hadamard transform. SIAM Journal of Matrix Analysis and Applications, 34: 1301-1340, 2013.
3. Chatterjee, S. and Hadi, A. S. Influential observations, high leverage point, and outliers in linear regression. Statistical Science, 1 (3):379-416, 2006.
4. Chatterjee, S. and Hadi, A.S. Sensitivity Analysis in Linear Regression. John Wiley & Sons, New York, 1988.
5. Drineas, P., Mahoney, M.W., and Muthukrishnan, S. Sampling algorithms for f2 regression and applications. In Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1127-1136, 2006.
6. Drineas, P., Mahoney, M. W., Muthukrishnan, S., and Sar-los, T. Faster least squares approximation. Numerical Mathematics, 117:219-249, 2011.
7. Drineas, P., Magdon-Ismail, M., Mahoney, M. W., and Woodruff, D. P. Fast approximation of matrix coherence and statistical leverage. Journal of Machine Learning Research, 13:3475-3506, 2012.
8. Golub, G.H. and Loan, C.F. Van. Matrix Computations. Johns Hopkins University Press, Baltimore, 1996.
9. Hample, F. R., Ronchetti, E. M., Roisseeuw, P. J., and Sta-hel, W. A. Robust Statisitcs: The Approach Based on Influence Functions. John Wiley & Sons, New York, 1986.
10. Hedayat, A. and Wallis, W. D. Hadamard matrices and their applications. Annals of Statistics, 6(6): 1184-1238, 1978.
11. Hoaglin, D.C. and Welsch, R.E. The hat matrix in regression and ANOVA. The American Statistician, 32(1): 17-22, 1978.
12. Huber, P. J. and Ronchetti, E. M. Robust Statisitcs. John Wiley & Sons, New York, 1981.
13. Lehmann, E. L. Elements of Large-Sample Theory. Springer Verlag, New York, 1998.
14. Ma, P., Mahoney, M. W., and Yu, B. A statistical perspective on algorithmic leveraging. JMLR, 2015. To appear.
15. Mahoney, M. W. Randomized algorithms for matrices and data. Foundations and Trends in Machine Learning. NOW Publishers, Boston, 2011. Also available at: arXiv: 1104.5557.
16. Meng, X., Saunders, M. A., and Mahoney, M. W. LSRN: A parallel iterative solver for strongly over-or under-determined systems. SIAM Journal on Scientific Computing, 36(2):C95-C118, 2014.
17. Meyer, Carl D. Matrix Analysis and Applied Linear Algebra. SIAM, 2000.
18. Pilanci, M. and Wainwright, M. J. Iterative Hessian sketch: Fast and accurate solution approximation for constrained least-squares. Technical report, 2014. Preprint: arXiv: 1411.0347.
19. Raskutti, G. and Mahoney, M. W. A statistical perspective on randomized sketching for ordinary least-squares. Technical report, 2014. Preprint: arXiv: 1406.5986.
20. Royall, R. M. On finite population sampling theory under certain linear regression models. Biometrika, 57:377-387, 1970.
21. Zavlavsky, A. M., Zheng, H., and Adams, J. Optimal sample allocation for design-consistent regression in a cancer services survey when design variables are known for aggregates. Survey Mehodology, 34(l):65-78, 2008.