The lasso under poisson-like heteroscedasticity

Statistica Sinica

Volumn 23, Issue 1, 2013, Pages 99-118

  Jia, Jinzhu ^a   Rohe, Karl ^b   Yu, Bin ^c  

^a PEKING UNIVERSITY   (China)

^b University of Wisconsin Madison   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Heteroscedasticity; Lasso; Poisson like model; Sign consistency

Indexed keywords

EID: 84884243793     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: 10.5705/ss.2010.254     Document Type: Article

References (27)

1. Candes, E. and Tao, T. (2005). Decoding by linear programming. IEEE Trans. Inform. Theory 51, 4203-4215.
2. Candes, E. and Tao, T. (2006). Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inform. Theory 52, 489-509.
3. Candes, E. and Tao, T. (2007). The Dantzig selector: statistical estimation when p is much larger than n. Ann. Statist. 35, 2313-2351.
4. Chen, S., Donoho, D. L. and Saunders., M. A. (1998). Atomic decomposition by basis pursuit. J. Sci. Computing 20, 33-61.
5. Davidson, K. R. and Szarek, S. J. (2001). Local operator theory, random matrices, and Banach spaces. In Handbook of Banach Spaces, volume 1, 317-366. Elsevier, Amsterdan.
6. Donoho, D. L. (2004). For most large undetermined system of linear equations the minimal l1- norm near-solution is also the sparsest solution. Technical report, Statistics Department, Stanford University.
7. Donoho, D. L., Elad, M. and Temlyakov, V. M. (2006). Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans. Inform. Theory 52, 6-18.
8. Donoho, D. L. and Huo., X. (2001). Uncertainty principles and ideal atomic decomposition. IEEE Trans. Inform. Theory 47, 2845-2862.
9. Efron, B., Hastie, T., Johnstone, I. and Tibshirani, R. (2004). Least angle regression. Ann. Statist. 32, 407-451.
10. Elad, M. and Bruckstein., A. M. (2002). A generalized uncertainty principle and sparse representation in pairs of bases. IEEE Trans. Inform. Theory 48, 2558-2567.
11. Feuer, A. and Nemirovski, A. (2003). On sparse representation in pairs of bases. IEEE Trans. Inform. Theory 49, 1579-1581.
12. Fan, J. and Lv, J. (2010). A selective overview of variable selection in high dimensional feature space. Statist. Sinica 20, 101-148.
13. Fessler, J. (2000). Statistical image reconstruction methods for transmission tomography. Hand-book of Medical Imaging 2, 1-70.
14. Fuchs, J. (2005). Recovery of exact sparse representations in the presence of bounded noise. IEEE Trans. Inform. Theory 51, 3601-3608.
15. Knight, K. and Fu, W. J. (2000). Asymptotics for lasso-type estimators. Ann. Statist. 28, 1356-1378.
16. Lustig, M., Donoho, D., Santos, J., and Pauly, J. (2008). Compressed sensing MRI. IEEE Signal Processing Magazine 25, 72-82.
17. Meinshausen, N. and Buhlmann, P. (2006). High-dimensional graphs and variable selection with the lasso. Ann. Statist. 34, 1436-1462.
18. Osborne, M. R., Presnell, B. and Turlach, B. A. (2000). On the lasso and its dual. J. Comput. Graph. Statist. 9, 319-37.
19. Rosset, S. (2004). Tracking curved regularized optimization solution paths. NIPS.
20. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B 58, 267-288.
21. Tropp, J. (2004). Greed is good: algorithmic results for sparse approximation. IEEE Trans. Inform. Theory 50, 2231-2242.
22. Tropp, J. (2006). Just relax: Convex programming methods for identifying sparse signals in noise. IEEE Trans. Inform. Theory 52, 1030-1051.
23. Vardi, Y., Shepp, L. and Kaufman, L. (1985). A statistical model for positron emission tomography. J. Amer. Statist. Assoc. 80, 8-20.
24. Wainwright, M. (2009). Sharp thresholds for high-dimensional and noisy sparsity recovery usingconstrained quadratic programming (Lasso). IEEE Trans. Inform. Theory 55, 2183-2202.
25. Zhao, P. and Yu, B. (2006). On model selection consistency of lasso. J. Mach. Learn. Res. 7, 2541-2563.
26. Zhao, P. and Yu, B. (2007). Stagewise lasso. J. Mach. Learn. Res. 8, 2701-2726.
27. Zou, H. (2006). The adaptive lasso and its oracle properties. J. Amer. Statist. Assoc. 101, 1418-1429.