Robust nonparametric regression via sparsity control with application to load curve data cleansing

IEEE Transactions on Signal Processing

Volumn 60, Issue 4, 2012, Pages 1571-1584

  Mateos, Gonzalo ^a   Giannakis, Georgios B ^a  

^a University of Minnesota   (United States)

Author keywords

Lasso; load curve cleansing; nonparametric regression; outlier rejection; sparsity; splines

Indexed keywords

LASSO; LOAD CURVES; NONPARAMETRIC REGRESSION; OUTLIER REJECTION; SPARSITY;

COMPUTER SIMULATION; ESTIMATION; RELAXATION PROCESSES; SPLINES;

STATISTICS;

EID: 84858326764     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2011.2181837     Document Type: Article

References (50)

1. U.S. Congress, Act of the Publ. L. No. 110-140, H.R. 6, Energy Independence and Security Act of 2007 Dec. 2007 [Online]. Available: http://www.gpo.gov/fdsys/pkg/PLAW-110publ140/content- detail.html
2. The Smart Grid: An Introduction United States Department of Energy, Office of Electricity Delivery and Energy Reliability, Jan. 2010 [Online]. Available: http://www.oe.energy.gov/1165.htm
3. M. S. Asif and J. Romberg, "Dynamic updating for l1 minimization," IEEE Sel. Topics Signal Process., vol. 4, no. 2, pp. 421-434, 2010.
4. D. P. Bertsekas, Nonlinear Programming, 2nd ed. Belmont, MA: Athena Scientific, 1999.
5. E. J. Candes and P. A. Randall, "Highly robust error correction by convex programming," IEEE Trans. Inf. Theory, vol. 54, no. 7, pp. 2829-2840, 2008.
6. E. J. Candes and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4203-4215, 2005.
7. E. J. Candes, M. B. Wakin, and S. Boyd, "Enhancing sparsity by reweighted minimzation," J. Fourier Anal. Appl., vol. 14, pp. 877-905, Dec. 2008.
8. J. Chen, W. Li, A. Lau, J. Cao, and K. Eang, "Automated load curve data cleansing in power systems," IEEE Trans. Smart Grid, vol. 1, pp. 213-221, Sep. 2010.
9. S. S. Chen,D. L. Donoho, andM.A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput., vol. 20, pp. 33-61, 1998.
10. C. C. Chuang, S. F. Fu, J. T. Jeng, and C. C. Hsiao, "Robust support vector regression networks for function approximation with outliers," IEEE Trans. Neural Netw., vol. 13, pp. 1322-1330, Jun. 2002.
11. D. D. Cox, "Asymptotics for M-type smoothing splines," Ann. Stat., vol. 11, pp. 530-551, 1983.
12. J. Duchon, Splines Minimizing Rotation-Invariant Semi-Norms in Sobolev Spaces. New York: Springer-Verlag, 1977.
13. B. Efron, T. Hastie, I. M. Johnstone, and R. Tibshirani, "Least angle regression," Ann. Stat., vol. 32, pp. 407-499, 2004.
14. T. Evgeniou, M. Pontil, and T. Poggio, "Regularization networks and support vectormachines," Adv. Comput.Math., vol. 13, pp. 1-50, 2000.
15. J. Fan and R. Li, "Variable selection via nonconcave penalized likelihood and its oracle properties," J. Amer. Stat. Assoc., vol. 96, pp. 1348-1360, 2001.
16. M. Fazel, "Matrix rank minimization with applications," Ph.D. dissertation, Electr. Eng. Dept., Stanford Univ., Stanford, CA, 2002.
17. J. Friedman, T. Hastie, H. Hofling, and R. Tibshirani, "Pathwise coordinate optimization," Ann. Appl. Stat., vol. 1, pp. 302-332, 2007.
18. J. Friedman, T. Hastie, and R. Tibshirani, "Regularized paths for generalized linear models via coordinate descent," J. Stat. Softw., vol. 33, 2010 [Online]. Available: http://www.jstatsoft.org/v33/i01
19. J. J. Fuchs, "An inverse problem approach to robust regression," in Proc. Int. Conf. Acoust., Speech, Signal Process., Phoenix, AZ, Mar. 1999, pp. 180-188.
20. P. Garrigues and L. El Ghaoui, "Recursive Lasso: A homotopy algorithm for Lasso with online observations," presented at the Conf. Neural Inf. Process. Syst., Vancouver, Canada, Dec. 2008.
21. G. B. Giannakis, G. Mateos, S. Farahmand, V. Kekatos, and H. Zhu, "USPACOR: Universal sparsity-controlling outlier rejection," in Proc. Int. Conf. Acoust., Speech, Signal Process., Prague, Czech Republic, May 2011, pp. 1952-1955.
22. R. Griesse and D. A. Lorenz, "A semismooth Newton method for Tikhonov functionals with sparsity constraints," Inverse Problems, vol. 24, pp. 1-19, 2008.
23. S. R. Gunn, Matlab SVM Toolbox, 1997 [Online]. Available: http:// www.isis.ecs.soton.ac.uk/resources/svminfo
24. T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning, 2nd ed. New York: Springer, 2009.
25. S. G. Hauser, "Vision for the smart grid," presented at the U.S. Department of Energy Smart Grid R&D Roundtable Meeting, Washington DC, Dec. 9, 2009.
26. P. J. Huber and E. M. Ronchetti, Robust Statistics. New York:Wiley, 2009.
27. Y. Jin and B. D. Rao, "Algorithms for robust linear regression by exploiting the connection to sparse signal recovery," in Proc. Int. Conf. Acoust., Speech, Signal Process., Dallas, TX, Mar. 2010, pp. 3830-3833.
28. V. Kekatos and G. B. Giannakis, "From sparse signals to sparse residuals for robust sensing," IEEE Trans. Signal Process., vol. 59, pp. 3355-3368, Jul. 2010.
29. G. Kimbeldorf and G. Wahba, "A correspondence between bayesian estimation on stochastic processes and smoothing by splines," Ann. Math. Stat., vol. 41, pp. 495-502, 1970.
30. K. Lange, D. Hunter, and I. Yang, "Optimization transfer using surrogate objective functions (with discussion)," J. Comput. Graph. Stat., vol. 9, pp. 1-59, 2000.
31. Y. J. Lee,W. F. Heisch, and C. M. Huang, "e-SSVR: A smooth support vector machine for -insensitive regression," IEEE Trans. Knowl. Data Eng., vol. 17, pp. 678-685, 2005.
32. O. L. Mangasarian and D. R. Musicant, "Robust linear and support vector regression," IEEE Trans. Pattern Anal. Mach. Intell., vol. 22, pp. 950-955, Sep. 2000.
33. S. Mukherjee, E. Osuna, and F. Girosi, "Nonlinear prediction of chaotic time series using a support vector machine," in Proc. Workshop Neural Netw. Signal Process., Amelia Island, FL, 1997, pp. 24-26.
34. B. K. Natarajan, "Sparse approximate solutions to linear systems," SIAM J. Comput., vol. 24, pp. 227-234, 1995.
35. T. Poggio and F. Girosi, "A theory of networks for approximation and learning," Artificial Intelligence Lab.,Massachusetts Inst. of Technology, Cambridge, A. I.Memo No. 1140, 1989, "A theory of networks for approximation and learning,".
36. P. J. Rousseeuw and K. V. Driessen, "Computing LTS regression for large data sets," Data Mining Knowl. Discovery, vol. 12, pp. 29-45, 2006.
37. P. J. Rousseeuw and A. M. Leroy, Robust Regression and Outlier Detection. New York: Wiley, 1987.
38. A. J. Smola and B. Scholkopf, "A tutorial on support vector regression," Royal Holloway College, London, Neuro COLT Tech. Rep. TR-1998-030, 1998.
39. R. Tibshirani, "Regression shrinkage and selection via the lasso," J. Royal Stat. Soc B, vol. 58, pp. 267-288, 1996.
40. A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems. Washington DC: W. H. Winston, 1977.
41. J. Tropp, "Just relax: Convex programming methods for identifying sparse signals," IEEE Trans. Inf. Theory, vol. 51, pp. 1030-1051, Mar. 2006.
42. M. Unser, "Splines: A perfect fit for signal and image processing," IEEE Signal Process. Mag., vol. 16, pp. 22-38, Nov. 1999.
43. V. Vapnik, Statistical Learning Theory. New York: Wiley, 1998.
44. G. Wahba, Spline Models for Observational Data. Philadelphia, PA: SIAM, 1990.
45. G. Wahba and J. Wendelberger, "Some new mathematical methods for variational objective analysis using splines and cross validation," Month. Weather Rev., vol. 108, pp. 1122-1145, 1980.
46. J. Wright and Y. Ma, "Dense error correction via -minimization," IEEE Trans. Inf. Theory, vol. 56, no. 7, pp. 3540-3560, 2010.
47. S. J. Wright, R. D. Nowak, and M. A. T. Figueiredo, "Sparse reconstruction by separable approximation," IEEE Trans. Signal Process., vol. 57, pp. 2479-2493, Jul. 2009.
48. T. Wu and K. Lange, "Coordinate descent algorithms for lasso penalized regression," Ann. Appl. Stat., vol. 2, pp. 224-244, 2008.
49. J. Zhu, S. C. H. Hoi, and M. R. T. Lyu, "Robust regularized kernel regression," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 38, pp. 1639-1644, Dec. 2008.
50. H. Zou, "The adaptive Lasso and its oracle properties," J. Amer. Stat. Assoc., vol. 101, no. 476, pp. 1418-1429, 2006.