Regularized matrix regression

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 76, Issue 2, 2014, Pages 463-483

  Zhou, Hua ^a   Li, Lexin ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Electroencephalography; Multi dimensional array; Nesterov method; Nuclear norm; Spectral regularization; Tensor regression

Indexed keywords

EID: 84893793864     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/rssb.12031     Document Type: Article

References (46)

1. Akaike, H. (1974) A new look at the statistical model identification. IEEE Trans. Autom. Control, 19, 716-723.
2. Allen, G., Grosenick, L. and Taylor, J. (2011) A generalized least squares matrix decompositionRice University, Houston. Preprint arXiv:1102.3074.
3. American Electroencephalographic Society (1991) American Electroencephalographic Society guidelines for standard electrode position nomenclature. J. Clin. Neurophysiol., 8, 200-202.
4. Armagan, A., Dunson, D. and Lee, J. (2013) Generalized double Pareto shrinkageStatist. Sin.23, 119-143.
5. Beck, A. and Teboulle, M. (2009a) A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imgng Sci., 2, 183-202.
6. Beck, A. and Teboulle, M. (2009b) Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. Trans. Image Process., 18, 2419-2434.
7. Borwein, J. M. and Lewis, A. S. (2006) Convex Analysis and Nonlinear Optimization, 2nd edn. New York: Springer.
8. Caffo, B. S., Crainiceanu, C. M., Verduzco, G., Joel, S., Mostafsky, S. H., Bassett, S. S and Pekar, J. J. (2010) Two-stage decompositions for the analysis of functional connectivity for fMRI with application to Alzheimer's disease risk. NeuroImage, 51, 1140-1149.
9. Cai, J.-F., Candès, E. J. and Shen, Z. (2010) A singular value thresholding algorithm for matrix completion. SIAM J. Optimizn, 20, 1956-1982.
10. Candès, E. J. and Recht, B. (2009) Exact matrix completion via convex optimization. Found. Comput. Math., 9, 717-772.
11. Candès, E. J., Wakin, M. B. and Boyd, S. P. (2008) Enhancing sparsity by reweighted l1 minimization. J. Four. Anal. Appl., 14, 877-905.
12. Chen, S. S., Donoho, D. L. and Saunders, M. A. (2001) Atomic decomposition by basis pursuit. SIAM Rev., 43, 129-159.
13. Chiquet, J., Grandvalet, Y. and Charbonnier, C. (2012) Sparsity with sign-coherent groups of variables via the cooperative-lasso. Ann. Appl. Statist., 6, 795-830.
14. Crainiceanu, C. M., Caffo, B. S., Luo, S., Zipunnikov, V. M. and Punjabi, N. M. (2011) Population value decomposition, a framework for the analysis of image populations. J. Am. Statist. Ass., 106, 775-790.
15. Donoho, D. L. and Johnstone, I. M. (1994) Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81, 425-455.
16. Efron, B. (2004) The estimation of prediction error: covariance penalties and cross-validation (with comments). J. Am. Statist. Ass., 99, 619-642.
17. Efron, B., Hastie, T., Johnstone, I. and Tibshirani, R. (2004) Least angle regression (with discussion). Ann. Statist., 32, 407-499.
18. Fan, J. and Li, R. (2001) Variable selection via nonconcave penalized likelihood and its oracle properties. J. Am. Statist. Ass., 96, 1348-1360.
19. Frank, I. E. and Friedman, J. H. (1993) A statistical view of some chemometrics regression tools. Technometrics, 35, 109-135.
20. Golub, G. H. and Van Loan, C. F. (1996) Matrix Computations, 3rd edn. Baltimore: Johns Hopkins University Press.
21. Hoerl, A. E. and Kennard, R. W. (1970) Ridge regression: biased estimation for nonorthogonal problems. Technometrics, 12, 55-67.
22. Hung, H. and Wang, C.-C. (2013) Matrix variate logistic regression model with application to eeg data. Biostatistics, 14, 189-202.
23. Johnstone, I. M. (2001) On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist., 29, 295-327.
24. Lange, K. (2004) Optimization. New York: Springer.
25. Li, B., Kim, M. K. and Altman, N. (2010) On dimension folding of matrix- or array-valued statistical objects. Ann. Statist., 38, 1094-1121.
26. Magnus, J. R. and Neudecker, H. (1999) Matrix Differential Calculus with Applications in Statistics and Econometrics. Chichester: Wiley.
27. Marshall, A. W., Olkin, I. and Arnold, B. C. (2011) Inequalities: Theory of Majorization and Its Applications, 2nd edn. New York: Springer.
28. Mazumder, R., Hastie, T. and Tibshirani, R. (2010) Spectral regularization algorithms for learning large incomplete matrices. J. Mach. Learn. Res., 11, 2287-2322.
29. McCullagh, P. and Nelder, J. A. (1983) Generalized Linear Models. London: Chapman and Hall.
30. Nemirovski, A. (1994) Efficient methods in convex programming. (Available from http://www2.isye.gatech.edu/~nemirovs/Lect__ECMO.pdf.)
31. Nesterov, Y. (1983) A method of solving a convex programming problem with convergence rate O(1/k2). Sov. Math. Dokl., 27, 372-376.
32. Nesterov, Y. (2004) Introductory Lectures on Convex Optimization. Boston: Kluwer.
33. Nocedal, J. and Wright, S. J. (2006) Numerical Optimization, 2nd edn. New York: Springer.
34. Qiu, P. (2005) Image Processing and Jump Regression Analysis. New York: Wiley.
35. Qiu, P. (2007) Jump surface estimation, edge detection, and image restoration. J. Am. Statist. Ass., 102, 745-756.
36. Recht, B., Fazel, M. and Parrilo, P. A. (2010) Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Rev., 52, 471-501.
37. Schwarz, G. (1978) Estimating the dimension of a model. Ann. Statist., 6, 461-464.
38. Stein, C. M. (1981) Estimation of the mean of a multivariate normal distribution. Ann. Statist., 9, 1135-1151.
39. Tibshirani, R. (1996) Regression shrinkage and selection via the lasso. J. R. Statist. Soc. B, 58, 267-288.
40. Tibshirani, R., Saunders, M., Rosset, S., Zhu, J. and Knight, K. (2005) Sparsity and smoothness via the fused lasso. J. R. Statist. Soc. B, 67, 91-108.
41. Yuan, M. and Lin, Y. (2006) Model selection and estimation in regression with grouped variables. J. R. Statist. Soc. B, 68, 49-67.
42. Zhang, C.-H. (2010) Nearly unbiased variable selection under minimax concave penalty. Ann. Statist., 38, 894-942.
43. Zhang, X., Begleiter, H., Porjesz, B., Wang, W. and Litke, A. (1995) Event related potentials during object recognition tasks. Brain Res. Bull., 38, 531-538.
44. Zhou, H., Li, L. and Zhu, H. (2013) Tensor regression with applications in neuroimaging data analysisJ. Am. Statist. Ass.
45. Zou, H. and Hastie, T. (2005) Regularization and variable selection via the elastic net. J. R. Statist. Soc. B, 67, 301-320.
46. Zou, H., Hastie, T. and Tibshirani, R. (2007) On the "degrees of freedom" of the lasso. Ann. Statist., 35, 2173-2192.