LASSO with non-linear measurements is equivalent to one with linear measurements

Advances in Neural Information Processing Systems

Volumn 2015-January, Issue , 2015, Pages 3420-3428

  Thrampoulidis, Christos ^a   Abbasi, Ehsan ^a   Hassibi, Babak ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ESTIMATION; INFORMATION SCIENCE;

CONSTANT OF PROPORTIONALITY; ESTIMATION PERFORMANCE; LINEAR MEASUREMENTS; MEASUREMENT FUNCTION; NONLINEAR FUNCTIONS; NONLINEAR MEASUREMENT; QUANTIZED MEASUREMENTS; REGULARIZATION PARAMETERS;

UNCERTAINTY ANALYSIS;

EID: 84965170219     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (25)

1. Francis R Bach. Structured sparsity-inducing norms through submodular functions. In Advances in Neural Information Processing Systems, pages 118-126, 2010.
2. Mohsen Bayati and Andrea Montanari. The lasso risk for gaussian matrices. Information Theory, IEEE Transactions on, 58(4):1997-2017, 2012.
3. Alexandre Belloni, Victor Chernozhukov, and Lie Wang. Square-root lasso: pivotal recovery of sparse signals via conic programming. Biometrika, 98(4):791-806, 2011.
4. David R. Brillinger. The identification of a particular nonlinear time series system. Biometrika, 64(3):509-515, 1977.
5. David R Brillinger. A generalized linear model with" gaussian" regressor variables. A Festschrift For Erich L. Lehmann, page 97, 1982.
6. Venkat Chandrasekaran, Benjamin Recht, Pablo A Parrilo, and Alan S Willsky. The convex geometry of linear inverse problems. Foundations of Computational Mathematics, 12(6):805-849, 2012.
7. David L Donoho and Iain M Johnstone. Minimax risk overl p-balls forl p-error. Probability Theory and Related Fields, 99(2):277-303, 1994.
8. David L Donoho, Lain Johnstone, and Andrea Montanari. Accurate prediction of phase transitions in compressed sensing via a connection to minimax denoising. IEEE transactions on information theory, 59(6):3396-3433, 2013.
9. David L Donoho, Arian Maleki, and Andrea Montanari. Message-passing algorithms for compressed sensing. Proceedings of the National Academy of Sciences, 106(45):18914-18919, 2009.
10. David L Donoho, Arian Maleki, and Andrea Montanari. The noise-sensitivity phase transition in compressed sensing. Information Theory, IEEE Transactions on, 57(10):6920-6941, 2011.
11. Alexandra L Garnham and Luke A Prendergast. A note on least squares sensitivity in single-index model estimation and the benefits of response transformations. Electronic J. of Statistics, 7:1983-2004, 2013.
12. n. Springer, 1988.
13. Marwa El Halabi and Volkan Cevher. A totally unimodular view of structured sparsity. arXiv preprint arXiv:1411.1990, 2014.
14. Hidehiko Ichimura. Semiparametric least squares (sls) and weighted sls estimation of single-index models. Journal of Econometrics, 58(1):71-120, 1993.
15. Ker-Chau Li and Naihua Duan. Regression analysis under link violation. The Annals of Statistics, pages 1009-1052, 1989.
16. Samet Oymak, Christos Thrampoulidis, and Babak Hassibi. The squared-error of generalized lasso: A precise analysis. arXiv preprint arXiv:1311.0830, 2013.
17. Yaniv Plan and Roman Vershynin. The generalized lasso with non-linear observations. arXiv preprint arXiv:1502.04071, 2015.
18. Mihailo Stojnic. A framework to characterize performance of lasso algorithms. arXiv preprint arXiv:1303.7291, 2013.
19. Christos Thrampoulidis, Samet Oymak, and Babak Hassibi. Regularized linear regression: A precise analysis of the estimation error. In Proceedings of The 28th Conference on Learning Theory, pages 1683-1709, 2015.
20. Christos Thrampoulidis, Ashkan Panahi, Daniel Guo, and Babak Hassibi. Precise error analysis of the lasso. In Acoustics, Speech and Signal Processing (ICASSP), 2015 IEEE International Conference on, pages 3467-3471.
21. 2-lasso. In Information Theory (ISIT), 2015 IEEE International Symposium on, pages 2021-2025. IEEE, 2015.
22. Robert Tibshirani. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological), pages 267-288, 1996.
23. Robert Tibshirani, Michael Saunders, Saharon Rosset, Ji Zhu, and Keith Knight. Sparsity and smoothness via the fused lasso. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(1):91-108, 2005.
24. Xinyang Yi, Zhaoran Wang, Constantine Caramanis, and Han Liu. Optimal linear estimation under unknown nonlinear transform. arXiv preprint arXiv:1505.03257, 2015.
25. Ming Yuan and Yi Lin. Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 68(1):49-67, 2006.