Sparse Modeling: Theory, Algorithms, and Applications

Sparse Modeling: Theory, Algorithms, and Applications

Volumn , Issue , 2014, Pages 1-231

  Rish, Irina ^a   Grabarnik, Genady Ya ^b  

^a IBM   (United States)

^b ST JOHN'S UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85051039341     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1201/b17758     Document Type: Book

References (338)

1. Adamczak, R., Litvak, A., Pajor, A., Tomczak-Jaegermann, N., 2011. Restricted isometry property of matrices with independent columns and neighborly polytopes by random sampling. Constructive Approximation 34 (1), 61-88.
2. Aharon, M., Elad, M., Bruckstein, A., 2006a. K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Transactions on Signal Processing 54 (11), 4311-4322.
3. Aharon, M., Elad, M., Bruckstein, A., 2006b. On the uniqueness of overcomplete dictionaries, and a practical way to retrieve them. Linear algebra and its applications 416 (1), 48-67.
4. Antoniadis, A., Fan, J., 2001. Regularization of wavelet approximations. Journal of the American Statistical Association 96 (455).
5. Asadi, N. B., Rish, I., Scheinberg, K., Kanevsky, D., Ramabhadran, B., 2009. MAP approach to learning sparse Gaussian Markov networks. In: Proc. of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). pp. 1721-1724.
6. Asif, M., Romberg, J., 2010. On the Lasso and Dantzig selector equivalence. In: Proc. of the 44th Annual Conference on Information Sciences and Systems (CISS). IEEE, pp. 1-6.
7. Atia, G., Saligrama, V., March 2012. Boolean compressed sensing and noisy group testing. IEEE Transactions on Information Theory 58 (3), 1880-1901.
8. Ausiello, G., Protasi, M., Marchetti-Spaccamela, A., Gambosi, G., Crescenzi, P., Kann, V., 1999. Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties. Springer-Verlag New York.
9. Bach, F., 2008a. Bolasso: Model consistent Lasso estimation through the bootstrap. In: Proc. of the 25th International Conference on Machine Learning (ICML). pp. 33-40.
10. Bach, F., 2008b. Consistency of the group Lasso and multiple kernel learning. Journal of Machine Learning Research 9, 1179-1225.
11. Bach, F., June 2008c. Consistency of trace norm minimization. Journal of Machine Learning Research 9, 1019-1048.
12. Bach, F., 2010. Self-concordant analysis for logistic regression. Electronic Journal of Statistics 4, 384-414.
13. Bach, F., Jenatton, R., Mairal, J., Obozinski, G., 2012. Optimization with sparsity-inducing penalties. Foundations and Trends in Machine Learning 4 (1), 1-106.
14. Bach, F., Lanckriet, G., Jordan, M., 2004. Multiple kernel learning, conic duality, and the SMO algorithm. In: Proc. of the Twenty-first International Conference on Machine Learning (ICML).
15. Bach, F., Mairal, J., Ponce, J., 2008. Convex sparse matrix factorizations. arXiv preprint arXiv:0812.1869.
16. Bakin, S., 1999. Adaptive regression and model selection in data mining problems. Ph.D. thesis, Australian National University, Canberra, Australia.
17. Balasubramanian, K., Yu, K., Lebanon, G., 2013. Smooth sparse coding via marginal regression for learning sparse representations. In: Proc. of the International Conference on Machine Learning (ICML). pp. 289-297.
18. Baliki, M., Geha, P., Apkarian, A., 2009. Parsing pain perception between nocicep-tive representation and magnitude estimation. Journal of Neurophysiology 101, 875-887.
19. Baliki, M., Geha, P., Apkarian, A., Chialvo, D., 2008. Beyond feeling: Chronic pain hurts the brain, disrupting the default-mode network dynamics. The Journal of Neuroscience 28 (6), 1398-1403.
20. Banerjee, A., Merugu, S., Dhillon, I., Ghosh, J., April 2004. Clustering with Bregman divergences. In: Proc. of the Fourth SIAM International Conference on Data Mining. pp. 234-245.
21. Banerjee, A., Merugu, S., Dhillon, I. S., Ghosh, J., October 2005. Clustering with Bregman divergences. Journal of Machine Learning Research 6, 1705-1749.
22. Banerjee, O., El Ghaoui, L., d’Aspremont, A., March 2008. Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data. Journal of Machine Learning Research 9, 485-516.
23. Banerjee, O., Ghaoui, L. E., d’Aspremont, A., Natsoulis, G., 2006. Convex optimization techniques for fitting sparse Gaussian graphical models. In: Proc. of the 23rd International Conference on Machine Learning (ICML). pp. 89-96.
24. Baraniuk, R., Davenport, M., DeVore, R., Wakin, M., 2008. A simple proof of the restricted isometry property for random matrices. Constructive Approximation 28 (3), 253-263.
25. Beck, A., Teboulle, M., 2009. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sciences 2 (1), 183-202.
26. Bengio, S., Pereira, F., Singer, Y., Strelow, D., 2009. Group sparse coding. In: Proc. of Neural Information Processing Systems (NIPS). Vol. 22. pp. 82-89.
27. Bertsekas, D., 1976. On the Goldstein-Levitin-Polyak gradient projection method. IEEE Transactions on Automatic Control 21 (2), 174-184.
28. Besag, J., 1974. Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society. Series B (Methodological) 36 (2), 192- 236.
29. Beygelzimer, A., Kephart, J., Rish, I., 2007. Evaluation of optimization methods for network bottleneck diagnosis. In: Proc. of the Fourth International Conference on Autonomic Computing (ICAC). Washington, DC, USA.
30. Beygelzimer, A., Rish, I., 2002. Inference complexity as a model-selection criterion for learning Bayesian networks. In: Proc. of the International Conference on Principles of Knowledge Representations and Reasoning (KR). pp. 558-567.
31. Bickel, P., December 2007. Discussion: The Dantzig selector: Statistical estimation when p is much larger than n. The Annals of Statistics 35 (6), 2352-2357.
32. Bickel, P., Ritov, Y., Tsybakov, A., 2009. Simultaneous analysis of Lasso and Dantzig selector. The Annals of Statistics 37 (4), 1705-1732.
33. Blomgren, P., Chan, F., 1998. Color TV: total variation methods for restoration of vector-valued images. IEEE Transactions on Image Processing 7 (3), 304-309.
34. Blumensath, T., Davies, M. E., 2007. On the difference between orthogonal matching pursuit and orthogonal least squares. Unpublished manuscript.
35. Borwein, J., Lewis, A., Borwein, J., Lewis, A., 2006. Convex analysis and nonlinear optimization: Theory and examples. Springer, New York.
36. Boyd, S., Vandenberghe, L., 2004. Convex Optimization. Cambridge University Press, New York, NY, USA.
37. Bradley, D., Bagnell, J., 2008. Differentiable sparse coding. In: Proc. of Neural Information Processing Systems (NIPS). pp. 113-120.
38. Buhl, S., 1993. On the existence of maximum likelihood estimators for graphical Gaussian models. Scandinavian Journal of Statistics 20 (3), 263-270.
39. Bühlmann, P., van de Geer, S., 2011. Statistics for High-Dimensional Data: Methods, Theory and Applications. Springer.
40. 2 penalization. Electron. J. Statist. 2, 1153-1194.
41. Bunea, F., Tsybakov, A., Wegkamp, M., 2007. Sparsity oracle inequalities for the Lasso. Electron. J. Statist. 1, 169-194.
42. Cadima, J., Jolliffe, I., 1995. Loading and correlations in the interpretation of principle compenents. Journal of Applied Statistics 22 (2), 203-214.
43. 1 minimization approach to sparse precision matrix estimation. Journal of American Statistical Association 106, 594- 607.
44. Cai, T., Lv, J., December 2007. Discussion: The Dantzig selector: Statistical estimation when p is much larger than n. The Annals of Statistics 35 (6), 2365-2369.
45. Candès, E., 2008. The restricted isometry property and its implications for compressed sensing. Comptes Rendus Mathematique 346 (9), 589-592.
46. Candès, E., Plan, Y., 2011. A probabilistic and RIPless theory of compressed sensing. IEEE Transactions on Information Theory 57 (11), 7235-7254.
47. Candès, E., Recht, B., 2009. Exact matrix completion via convex optimization. Foundations of Computational Mathematics 9 (6), 717-772.
48. Candès, E., Romberg, J., Tao, T., February 2006a. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. on Information Theory 52 (2), 489-509.
49. Candès, E., Romberg, J., Tao, T., 2006b. Stable signal recovery from incomplete and inaccurate measurements. Communications on Pure and Applied Mathematics 59 (8), 1207-1223.
50. Candès, E., Tao, T., December 2005. Decoding by linear programming. IEEE Trans. on Information Theory 51 (12), 4203-4215.
51. Candès, E., Tao, T., 2006. Near optimal signal recovery from random projections: Universal encoding strategies? IEEE Trans. Inform. Theory 52 (12), 5406-5425.
52. Candès, E., Tao, T., 2007. The Dantzig selector: Statistical estimation when p is much larger than n. Annals of Statistics 35 (6), 2313-2351.
53. Carl, B., 1985. Inequalities of Bernstein-Jackson-type and the degree of compactness of operators in banach spaces. Annales de l’institut Fourier 35 (3), 79-118.
54. Carroll, M., Cecchi, G., Rish, I., Garg, R., Rao, A., 2009. Prediction and interpretation of distributed neural activity with sparse models. NeuroImage 44 (1), 112- 122.
55. Cecchi, G., Huang, L., Hashmi, J., Baliki, M., Centeno, M., Rish, I., Apkarian, A., 2012. Predictive dynamics of human pain perception. PLoS Computational Biology 8 (10).
56. Cecchi, G., Rish, I., Thyreau, B., Thirion, B., Plaze, M., Paillere-Martinot, M.-L., Martelli, C., Martinot, J.-L., Poline, J.-B., 2009. Discriminative network models of schizophrenia. In: Proc. of Neural Information Processing Systems (NIPS). Vol. 22. pp. 250-262.
57. Chafai, D., Guédon, O., Lecué, G., Pajor, A., 2012. Interactions between compressed sensing, random matrices, and high dimensional geometry. forthcoming book.
58. Chan, T., Shen, J., 2005. Image Processing and Analysis: Variational, Pde, Wavelet, and Stochastic Methods. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA.
59. Chandalia, G., Rish, I., 2007. Blind source separation approach to performance diagnosis and dependency discovery. In: Proc. of the 7th ACM SIGCOMM Conference on Internet Measurement (IMC). pp. 259-264.
60. Chen, S., Donoho, D., Saunders, M., 1998. Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing 20 (1), 33-61.
61. Cheraghchi, M., Guruswami, V., Velingker, A., 2013. Restricted isometry of Fourier matrices and list decodability of random linear codes. SIAM Journal on Computing 42 (5), 1888-1914.
62. Cichocki, A., Zdunek, R., Amari, S., 2006. New algorithms for non-negative matrix factorization in applications to blind source separation. In: Proc. of the IEEE International Conference on Acoustics, Speech and Signal Processing. Vol. 5. pp. 621-624.
63. Cohen, A., Dahmen, W., DeVore, R., 2009. Compressed sensing and best k-term approximation. Journal of the American Mathematical Society 22 (1), 211-231.
64. Collins, M., Dasgupta, S., Schapire, R., 2001. A generalization of principal component analysis to the exponential family. In: Proc. of Neural Information Processing Systems (NIPS). MIT Press.
65. Combettes, P., Pesquet, J.-C., 2011. Fixed-Point Algorithms for Inverse Problems in Science and Engineering. Chapter: Proximal Splitting Methods in Signal Processing. Springer-Verlag.
66. Combettes, P., Wajs, V., 2005. Signal recovery by proximal forward-backward splitting. SIAM Journal on Multiscale Modeling and Simulation 4, 1168-1200.
67. Cowell, R., Dawid, P., Lauritzen, S., Spiegelhalter, D., 1999. Probabilistic Networks and Expert Systems. Springer.
68. Cox, D., Wermuth, N., 1996. Multivariate Dependencies: Models, Analysis and Interpretation. Chapman and Hall.
69. Dai, W., Milenkovic, O., 2009. Subspace pursuit for compressive sensing reconstruction. IEEE Trans. Inform. Theory 55 (5), 2230-2249.
70. d’Aspremont, A., Bach, F. R., Ghaoui, L. E., 2008. Optimal solutions for sparse principal component analysis. Journal of Machine Learning Research 9, 1269- 1294.
71. d’Aspremont, A., Ghaoui, L. E., Jordan, M. I., Lanckriet, G. R. G., 2007. A direct formulation for sparse PCA using semidefinite programming. SIAM Review 49 (3), 434-448.
72. Daubechies, I., Defrise, M., Mol, C. D., 2004. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Communications on Pure and Applied Mathematics 57, 1413-1457.
73. Dempster, A. P., March 1972. Covariance selection. Biometrics 28 (1), 157-175.
74. Dikmen, O., Févotte, C., 2011. Nonnegative dictionary learning in the exponential noise model for adaptive music signal representation. In: Proc. of Neural Information Processing Systems (NIPS). pp. 2267-2275.
75. Do, T., Gan, L., Nguyen, N., Tran, T., 2008. Sparsity adaptive matching pursuit algorithm for practical compressed sensing. In: Proc. of the 42nd Asilomar Conference on Signals, Systems, and Computers. pp. 581-587.
76. Donoho, D., April 2006a. Compressed sensing. IEEE Trans. on Information Theory 52 (4), 1289-1306.
77. 1-norm near-solution approximates the sparsest near-solution. Communications on Pure and Applied Mathematics 59 (7), 907-934.
78. 1-norm solution is also the sparsest solution. Communications on Pure and Applied Mathematics 59 (6), 797-829.
79. 1-norm solution is also the sparsest solution. Comm. Pure Appl. Math. 59 (6), 797-829.
80. 1 minimization. Proc. Natl. Acad. Sci. USA 100, 2197-2202.
81. Donoho, D., Elad, M., Temlyakov, V., 2006. Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans. Inform. Theory 52 (1), 6-18.
82. Donoho, D., Huo, X., 2001. Uncertainty principles and ideal atomic decomposition. IEEE Trans. Inform. Theory 47, 2845-2862.
83. Donoho, D., Stark, P., 1989. Uncertainty principles and signal recovery. SIAM J. Appl. Math. 49, 906-931.
84. Donoho, D., Tanner, J., 2009. Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367 (1906), 4273-4293.
85. Donoho, D., Tsaig, Y., Drori, I., Starck, J., 2012. Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit. IEEE Transactions on Information Theory 58 (2), 1094-1121.
86. Dorfman, R., 1943. The detection of defective members of large populations. The Annals of Mathematical Statistics 14 (4), 436-440.
87. Du, D., Hwang, F., 2000. Combinatorial group testing and its applications, 2nd edition. World Scientific Publishing Co., Inc., River Edge, NJ.
88. Duchi, J., Gould, S., Koller, D., 2008. Projected subgradient methods for learning sparse Gaussians. In: Proc. of Uncertainty in Artificial Intelligence (UAI).
89. Edwards, D., 2000. Introduction to Graphical Modelling, 2nd Edition. Springer.
90. Efron, B., Hastie, T., 2004. LARS software for R and Splus: http://www.stanford. edu/hastie/Papers/LARS/.
91. Efron, B., Hastie, T., Johnstone, I., Tibshirani, R., 2004. Least angle regression. Ann. Statist. 32 (1), 407-499.
92. Efron, B., Hastie, T., Tibshirani, R., December 2007. Discussion: The Dantzig selector: Statistical estimation when p is much larger than n. The Annals of Statistics 35 (6), 2358-2364.
93. Elad, M., 2006. Why simple shrinkage is still relevant for redundant representations? IEEE Transactions on Information Theory 52, 5559-5569.
94. Elad, M., 2010. Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing. Springer.
95. Elad, M., Aharon, M., 2006. Image denoising via sparse and redundant representations over learned dictionaries. IEEE Transactions on Image Processing 15 (12), 3736-3745.
96. Elad, M., Matalon, B., Zibulevsky, M., 2006. Image denoising with shrinkage and redundant representations. In: Proc. of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR). Vol. 2. IEEE, pp. 1924-1931.
97. Eldar, Y., Kutyniok, G. (editors), 2012. Compressed Sensing: Theory and Applications. Cambridge University Press.
98. Engan, K., Aase, S., Husoy, H., 1999. Method of optimal directions for frame design. In: Proc. of the International Conference on Acoustics, Speech, and Signal Processing (ICASSP). Vol. 5. pp. 2443-2446.
99. Fan, J., Li, R., 2005. Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 96, 1348-1360.
100. Fazel, M., Hindi, H., Boyd, S., 2001. A rank minimization heuristic with application to minimum order system approximation. In: Proc. of the 2001 American Control Conference. Vol. 6. IEEE, pp. 4734-4739.
101. Figueiredo, M., Nowak, R., 2003. An EM algorithm for wavelet-based image restoration. IEEE. Trans. Image Process. 12, 906-916.
102. Figueiredo, M., Nowak, R., 2005. A bound optimization approach to wavelet-based image deconvolution. In: Proc. of the IEEE International Conference on Image Processing (ICIP). Vol. 2. IEEE, pp. II-782.
103. p-balls for 0 < p ≤ 1. Journal of Complexity 26 (6), 629-640.
104. Foucart, S., Rauhut, H., 2013. A mathematical introduction to compressive sensing. Springer.
105. Frank, I., Friedman, J., 1993. A statistical view of some chemometrics regression tools. Technometrics 35 (2), 109-148.
106. Friedlander, M., Saunders, M., December 2007. Discussion: The Dantzig selector: Statistical estimation when p is much larger than n. The Annals of Statistics 35 (6), 2385-2391.
107. Friedman, J., Hastie, T., Hoefling, H., Tibshirani, R., 2007a. Pathwise coordinate optimization. Annals of Applied Statistics 2 (1), 302-332.
108. Friedman, J., Hastie, T., Tibshirani, R., 2007b. Sparse inverse covariance estimation with the graphical Lasso. Biostatistics.
109. Friedman, J., T. Hastie, T., Tibshirani, R., 2010. A note on the group Lasso and a sparse group Lasso. Tech. Rep. arXiv:1001.0736v1, ArXiv.
110. Friston, K., Holmes, A., Worsley, K., Poline, J.-P., Frith, C., Frackowiak, R., 1995. Statistical parametric maps in functional imaging: A general linear approach. Human brain mapping 2 (4), 189-210.
111. Fu, W., 1998. Penalized regressions: The bridge vs. the Lasso. Journal of Computational and Graphical Statistics 7 (3).
112. Fuchs, J., 2005. Recovery of exact sparse representations in the presence of bounded noise. IEEE Trans. Information Theory 51 (10), 3601-3608.
113. Garey, M., Johnson, D. S., 1979. Computers and intractability: A Guide to the theory of NP-completeness. Freeman, San Francisco.
114. Garnaev, A., Gluskin, E., 1984. The widths of a Euclidean ball. Dokl. Akad. Nauk USSR 277, 1048-1052, english transl. Soviet Math. Dokl. 30 (200-204).
115. Garrigues, P., Olshausen, B., 2010. Group sparse coding with a Laplacian scale mixture prior. In: Proc. of Neural Information Processing Systems (NIPS). pp. 676- 684.
116. Gaussier, E., Goutte, C., 2005. Relation between PLSA and NMF and implications. In: Proc. of the 28th annual international ACM SIGIR conference on Research and development in information retrieval. ACM, pp. 601-602.
117. Gilbert, A., Hemenway, B., Rudra, A., Strauss, M., Wootters, M., 2012. Recovering simple signals. In: Information Theory and Applications Workshop (ITA). pp. 382-391.
118. Gilbert, A., Strauss, M., 2007. Group testing in statistical signal recovery. Technometrics 49 (3), 346-356.
119. Goldstein, R., Alia-Klein, N., Tomasi, D., Honorio, J., Maloney, T., Woicik, P., Wang, R., Telang, F., Volkow, N., 2009. Anterior cingulate cortex hypoactivations to an emotionally salient task in cocaine addiction. Proceedings of the National Academy of Sciences, USA.
120. Gorodnitsky, F., Rao, B., 1997. Sparse signal reconstruction from limited data using FOCUSS: A reweighted norm minimization algorithm. IEEE Trans. Signal Proc. 45, 600-616.
121. Greenshtein, E., Ritov, Y., 2004. Persistence in high-dimensional linear predictor selection and the virtue of overparametrization. Bernoulli 10 (6), 971-988.
122. Gregor, K., LeCun, Y., 2010. Learning fast approximations of sparse coding. In: Proc. of the 27th International Conference on Machine Learning (ICML). pp. 399-406.
123. Gribonval, R., Nielsen, M., 2003. Sparse representations in unions of bases. IEEE Trans. Inform. Theory 49 (12), 3320-3325.
124. Grimmett, G. R., 1973. A theorem about random fields. Bulletin of the London Mathematical Society 5 (1), 81-84.
125. Guillamet, D., Vitrià, J., 2002. Non-negative matrix factorization for face recognition. In: Topics in Artificial Intelligence. Springer, pp. 336-344.
126. Hammersley, J., Clifford, P., 1971. Markov fields on finite graphs and lattices. unpublished manuscript.
127. Hastie, T., Tibshirani, R., Friedman, J., 2009. The elements of statistical learning: data mining, inference, and prediction, 2nd edition. New York: Springer-Verlag.
128. Haxby, J., Gobbini, M., Furey, M., Ishai, A., Schouten, J., Pietrini, P., 2001. Distributed and overlapping representations of faces and objects in ventral temporal cortex. Science 293 (5539), 2425-2430.
129. Heckerman, D., 1995. A tutorial on learning Bayesian networks. Tech. Rep. Tech. Report MSR-TR-95-06, Microsoft Research.
130. Ho, J., Xie, Y., Vemuri, B., 2013. On a nonlinear generalization of sparse coding and dictionary learning. In: Proc. of the International Conference on Machine Learning (ICML). pp. 1480-1488.
131. Ho, N.-D., 2008. Nonnegative matrix factorization algorithms and applications. Ph.D. thesis, École Polytechnique.
132. Hoerl, A., Kennard, R., 1988. Ridge regression. Encyclopedia of Statistical Sciences 8 (2), 129-136.
133. Honorio, J., Jaakkola, T., 2013. Inverse covariance estimation for high-dimensional data in linear time and space: Spectral methods for Riccati and sparse models. In: Proc. of Uncertainty in Artificial Intelligence (UAI).
134. Honorio, J., Ortiz, L., Samaras, D., Paragios, N., Goldstein, R., 2009. Sparse and locally constant Gaussian graphical models. In: Proc. of Neural Information Processing Systems (NIPS). pp. 745-753.
135. Honorio, J., Samaras, D., Rish, I., Cecchi, G., 2012. Variable selection for Gaussian graphical models. In: Proc. of the International Conference on Artificial Intelligence and Statistics (AISTATS). pp. 538-546.
136. Hoyer, P., 2004. Non-negative matrix factorization with sparseness constraints. Journal of Machine Learning Research 5, 1457-1469.
137. Hsieh, C.-J., Sustik, M., Dhillon, I., Ravikumar, P., Poldrack, R., 2013. BIG & QUIC: Sparse inverse covariance estimation for a million variables. In: Proc. of Neural Information Processing Systems (NIPS). pp. 3165-3173.
138. Huang, S., Li, J., Sun, L., Liu, J., Wu, T., Chen, K., Fleisher, A., Reiman, E., Ye, J., 2009. Learning brain connectivity of Alzheimer’s disease from neuroimaging data. In: Proc. of Neural Information Processing Systems (NIPS). Vol. 22. pp. 808-816.
139. Huang, S., Li, J., Ye, J., Fleisher, A., Chen, K., Wu, T., Reiman, E., 2013. The Alzheimer’s Disease Neuroimaging Initiative, 2013. A sparse structure learning algorithm for gaussian bayesian network identification from high-dimensional data. IEEE Transactions on Pattern Analysis and Machine Intelligence 35 (6), 1328- 1342.
140. Huber, P., 1964. Robust estimation of a location parameter. The Annals of Mathematical Statistics 35 (1), 73-101.
141. Ishwaran, H., Rao, J., 2005. Spike and slab variable selection: Frequentist and Bayesian strategies. Ann. Statist. 33 (2), 730-773.
142. Jacob, L., Obozinski, G., Vert, J.-P., 2009. Group Lasso with overlap and graph Lasso. In: Proc. of the 26th Annual International Conference on Machine Learning (ICML). pp. 433-440.
143. Jalali, A., Chen, Y., Sanghavi, S., Xu, H., 2011. Clustering partially observed graphs via convex optimization. In: Proc. of the 28th International Conference on Machine Learning (ICML). pp. 1001-1008.
144. James, G. M., Radchenko, P., Lv, J., 2009. DASSO: Connections between the Dantzig selector and Lasso. Journal of The Royal Statistical Society Series B 71 (1), 127-142.
145. Jenatton, R., 2011. Structured sparsity-inducing norms: Statistical and algorithmic properties with applications to neuroimaging. Ph.D. thesis, Ecole Normale Su-perieure de Cachan.
146. Jenatton, R., Audibert, J.-Y., Bach, F., 2011a. Structured variable selection with sparsity-inducing norms. Journal of Machine Learning Research 12, 2777-2824.
147. Jenatton, R., Gramfort, A., Michel, V., Obozinski, G., Bach, F., Thirion, B., 2011b. Multi-scale mining of fMRI data with hierarchical structured sparsity. In: Proceedings of the 2011 International Workshop on Pattern Recognition in NeuroImaging (PRNI). IEEE, pp. 69-72.
148. Jenatton, R., Mairal, J., Obozinski, G., Bach, F., 2011c. Proximal methods for hierarchical sparse coding. Journal of Machine Learning Research 12, 2297-2334.
149. Jenatton, R., Obozinski, G., Bach, F., 2010. Structured sparse principal component analysis. In: Proc. of International Conference on Artificial Intelligence and Statistics. pp. 366-373.
150. Ji, S., Xue, Y., Carin, L., June 2008. Bayesian compressive sensing. IEEE Trans. on Signal Processing 56 (6), 2346-2356.
151. Johnson, W., Lindenstrauss, J., 1984. Extensions of Lipschitz mappings into a Hilbert space. In: Conf. in Modern Analysis and Probability. Vol. 26. Amer. Math. Soc., Providence, RI, pp. 189-206.
152. Jolliffe, I., Trendafilov, N., Uddin, M., 2003. A modified principal component technique based on the Lasso. Journal of Computational and Graphical Statistics 12, 531-547.
153. Jordan, M., 2000. Graphical models. Statistical Science (Special Issue on Bayesian Statistics) 19, 140-155.
154. Kakade, S., Shamir, O., Sindharan, K., Tewari, A., 2010. Learning exponential families in high-dimensions: Strong convexity and sparsity. In: Proc. of the International Conference on Artificial Intelligence and Statistics (AISTATS). pp. 381- 388.
155. Kambadur, P., Lozano, A. C., 2013. A parallel, block greedy method for sparse inverse covariance estimation for ultra-high dimensions. In: Proc. of the International Conference on Artificial Intelligence and Statistics (AISTATS). pp. 351- 359.
156. Kannan, R., Lovász, L., Simonovits, M., 1997. Random walks and an O*(n5) volume algorithm for convex bodies. Random structures and algorithms 11 (1), 1-50.
157. Kasiviswanathan, S. P., Wang, H., Banerjee, A., Melville, P., 2012. Online L1-dictionary learning with application to novel document detection. In: Proc. of Neural Information Processing Systems (NIPS). pp. 2267-2275.
158. Kim, H., Park, H., 2007. Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis. Bioinfor-matics 23 (12), 1495-1502.
159. Kim, S., Xing, E., 2010. Tree-guided group Lasso for multi-task regression with structured sparsity. In: Proc. of the 27th International Conference on Machine Learning (ICML). pp. 543-550.
160. Kim, T., Shakhnarovich, G., Urtasun, R., 2010. Sparse coding for learning interpretable spatio-temporal primitives. In: Proc. of Neural Information Processing Systems (NIPS). pp. 1117-1125.
161. Kimeldorf, G., Wahba, G., 1971. Some results on Tchebycheffian spline function. J. Math. Anal. Applications 33, 82-95.
162. Kindermann, R., Snell, J., 1980. Markov Random Fields and Their Applications. American Mathematical Society.
163. Knight, K., Fu, W., 2000. Asymptotics for Lasso-type estimators. Ann. Statist. 28 (5), 1356-1378.
164. Koller, D., Friedman, N., 2009. Probabilistic Graphical Models: Principles and Techniques. MIT Press.
165. Koltchinskii, V., 2009. The Dantzig selector and sparsity oracle inequalities. Bernoulli 15 (3), 799-828.
166. Kotelnikov, V., 1933. On the transmission capacity of ether and wire in electric communications. Izd. Red. Upr. Svyazi RKKA (in Russian).
167. Kotelnikov, V., 2006. On the transmission capacity of ether and wire in electric communications (1933). Physics-Uspekhi 49 (7), 736-744.
168. Kreutz-Delgado, K., Murray, J., Rao, B., Engan, K., Lee, T.-W., Sejnowski, T., 2003. Dictionary learning algorithms for sparse representation. Neural Computation 15 (2), 349-396.
169. Kruskal, J., 1977. Three-way arrays: Rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics. Linear algebra and its applications 18 (2), 95-138.
170. Lanckriet, G., Cristianini, N., Bartlett, P., Ghaoui, L. E., Jordan, M., 2004. Learning the kernel matrix with semidefinite programming. Journal of Machine Learning Research 5, 27-72.
171. Lauritzen, S., 1996. Graphical Models. Oxford University Press.
172. Lawton, W., Sylvestre, E., 1971. Self modeling curve resolution. Technometrics 13 (3), 617-633.
173. Ledoux, M., Talagrand, M., 2011. Probability in Banach spaces: Isoperimetry and processes. Vol. 23. Springer.
174. Lee, H., Battle, A., Raina, R., Ng, A., 2006a. Efficient sparse coding algorithms. In: Proc. of Neural Information Processing Systems (NIPS). pp. 801-808.
175. Lee, J., Telang, F., Springer, C., Volkow, N., 2003. Abnormal brain activation to visual stimulation in cocaine abusers. Life Sciences.
176. 1-regularization. In: Proc. of Neural Information Processing Systems (NIPS). pp. 817-824.
177. Lesage, S., Gribonval, R., Bimbot, F., Benaroya, L., 2005. Learning unions of orthonormal bases with thresholded singular value decomposition. In: Proc. of the International Conference on Acoustics, Speech, and Signal Processing (ICASSP). Vol. 5. pp. 293-296.
178. Lewicki, M., Olshausen, B., 1999. A probabilistic framework for the adaptation and comparison of image codes. Journal of the Optical Society of America A: Optics, Image Science and Vision 16 (7), 1587-1601.
179. Lewicki, M., Sejnowski, T., 2000. Learning overcomplete representations. Neural Computation 12, 337-365.
180. Li, J., Tao, D., 2010. Simple exponential family PCA. In: Proc. of International Conference on Artificial Intelligence and Statistics (AISTATS). pp. 453-460.
181. Li, S. Z., Hou, X., Zhang, H., Cheng, Q., 2001. Learning spatially localized, parts-based representation. In: Proc. of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR). Vol. 1. IEEE, pp. I-207.
182. Lin, Y., Zhang, H., 2006. Component selection and smoothing in smoothing spline analysis of variance models. Annals of Statistics 34, 2272-2297.
183. Lin, Y., Zhu, S., Lee, D., Taskar, B., 2009. Learning sparse Markov network structure via ensemble-of-trees models. In: Proc. of the International Conference on Artificial Intelligence and Statistics (AISTATS). pp. 360-367.
184. Lions, P., Mercier, B., 1979. Splitting algorithms for the sum of two nonlinear operators. SIAM Journal on Numerical Analysis 16 (6), 964-979.
185. Liu, H., Palatucci, M., Zhang, J., 2009a. Blockwise coordinate descent procedures for the multi-task Lasso, with applications to neural semantic basis discovery. In: Proc. of the 26th Annual International Conference on Machine Learning (ICML). ACM, pp. 649-656.
186. Liu, H., Zhang, J., 2009. Estimation consistency of the group Lasso and its applications. Journal of Machine Learning Research-Proceedings Track 5, 376-383.
187. 2, 1-norm minimization. In: Proc. of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence (UAI). AUAI Press, pp. 339-348.
188. Lozano, A., Abe, N., Liu, Y., Rosset, S., 2009a. Grouped graphical Granger modeling methods for temporal causal modeling. In: Proc. of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. pp. 577-586.
189. Lozano, A., Swirszcz, G., Abe, N., 2009b. Grouped orthogonal matching pursuit for variable selection and prediction. In: Proc. of Neural Information Processing Systems (NIPS). pp. 1150-1158.
190. Lu, Z., 2009. Smooth optimization approach for sparse covariance selection. SIAM Journal on Optimization 19 (4), 1807-1827.
191. Lv, J., Fan, Y., 2009. A unified approach to model selection and sparse recovery using regularized least squares. The Annals of Statistics 37 (6A), 3498-3528.
192. Mairal, J., Bach, F., Ponce, J., Sapiro, G., 2009. Online dictionary learning for sparse coding. In: Proc. of the 26th Annual International Conference on Machine Learning (ICML). ACM, pp. 689-696.
193. Mairal, J., Bach, F., Ponce, J., Sapiro, G., 2010. Online learning for matrix factorization and sparse coding. Journal of Machine Learning Research 11, 19-60.
194. Mairal, J., Yu, B., 2012. Complexity analysis of the Lasso regularization path. In: Proc. of the 29th International Conference on Machine Learning (ICML). pp. 353- 360.
195. Malioutov, D., Çetin, M., Willsky, A., 2005. A sparse signal reconstruction perspective for source localization with sensor arrays. IEEE Transactions on Signal Processing 53 (8), 3010-3022.
196. Mallat, S., Davis, G., Zhang, Z., 1994. Adaptive time-frequency decompositions. SPIE Journal of Optical Engineering 33, 2183-2191.
197. Mallat, S., Zhang, Z., 1993. Matching pursuits with time-frequency dictionaries. IEEE Transactions on Signal Processing 41, 3397-3415.
198. Marlin, B., Murphy, K., 2009. Sparse Gaussian graphical models with unknown block structure. In: Proc. of the 26th Annual International Conference on Machine Learning (ICML). ACM, pp. 705-712.
199. Martinet, B., 1970. Régularisation d-inéquations variationnelles par approximations successives. Revue franaise d-informatique et de recherche opérationnelle, série rouge.
200. Matoušek, J., 2002. Lectures on discrete geometry. Springer Verlag.
201. Maurer, A., Pontil, M., Romera-Paredes, B., 2013. Sparse coding for multitask and transfer learning. In: Proc. of International Conference on Machine Learning (ICML). pp. 343-351.
202. Mccullagh, P., Nelder, J., 1989. Generalized Linear Models, 2nd ed. Chapman and Hall, London.
203. Meier, L., van de Geer, S., Bühlmann, P., 2008. The group Lasso for logistic regression. J. Royal Statistical Society: Series B 70 (1), 53-71.
204. Meinshausen, N., 2007. Relaxed Lasso. Computational Statistics and Data Analysis 52 (1), 374-293.
205. Meinshausen, N., Bühlmann, P., 2006. High dimensional graphs and variable selection with the Lasso. Annals of Statistics 34(3), 1436-1462.
206. Meinshausen, N., Bühlmann, P., 2010. Stability selection. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72 (4), 417-473.
207. Meinshausen, N., Rocha, G., Yu, B., 2007. Discussion: A tale of three cousins: Lasso, L2Boosting and Dantzig. The Annals of Statistics, 2373-2384.
208. Milman, V., Pajor, A., 1989. Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space. Geometric aspects of functional analysis, 64-104.
209. Milman, V., Schechtman, G., 1986. Asymptotic theory of finite dimensional normed spaces. Springer Verlag.
210. Mishra, B., Meyer, G., Bach, F., Sepulchre, R., 2013. Low-rank optimization with trace norm penalty. SIAM Journal on Optimization 23 (4), 2124-2149.
211. Mitchell, T., Hutchinson, R., Niculescu, R., Pereira, F., Wang, X., Just, M., Newman, S., 2004. Learning to decode cognitive states from brain images. Machine Learning 57, 145-175.
212. Moghaddam, B., Weiss, Y., Avidan, S., 2006. Generalized spectral bounds for sparse LDA. In: Proc. of the 23rd International Conference on Machine Learning (ICML). ACM, pp. 641-648.
213. Moreau, J., 1962. Fonctions convexes duales et points proximaux dans un es-pace hilbertien. Comptes-Rendus de l-Académie des Sciences de Paris, Série A, Mathèmatiques 255, 2897-2899.
214. Morioka, N., Shiníchi, S., 2011. Generalized Lasso based approximation of sparse coding for visual recognition. In: Proc. of Neural Information Processing Systems (NIPS). pp. 181-189.
215. Moussouris, J., 1974. Gibbs and Markov systems with constraints. Journal of statistical physics 10, 11-33.
216. Muthukrishnan, S., 2005. Data streams: Algorithms and applications. Now Publishers Inc.
217. Nardi, Y., Rinaldo, A., 2008. On the asymptotic properties of the group Lasso estimator for linear models. Electronic Journal of Statistics 2, 605-633.
218. Natarajan, K., 1995. Sparse approximate solutions to linear systems. SIAM J. Comput. 24, 227-234.
219. Needell, D., Tropp, J. A., 2008. Iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmon. Anal. 26, 301-321.
220. Needell, D., Vershynin, R., 2009. Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit. Foundations of Computational Mathematics 9, 317-334.
221. Negahban, S., Ravikumar, P., Wainwright, M., Yu, B., 2009. A unified framework for high-dimensional analysis of M-estimators with decomposable regularizers. In: Proc. of Neural Information Processing Systems (NIPS). pp. 1348-1356.
222. Negahban, S., Ravikumar, P., Wainwright, M., Yu, B., 2012. A unified framework for high-dimensional analysis of M-estimators with decomposable regularizers. Statistical Science 27 (4), 438-557.
223. Negahban, S., Wainwright, M., 2011. Estimation of (near) low-rank matrices with noise and high-dimensional scaling. The Annals of Statistics 39 (2), 1069-1097.
224. Nemirovsky, A., Yudin, D., 1983. Problem Complexity and Method Efficiency in Optimization. Wiley-Interscience Series in Discrete Mathematics, John Wiley & Sons, New York.
225. 2) (in Russian). Dokl. Akad. Nauk SSSR 269, 543-547.
226. Nesterov, Y., 2005. Smooth minimization of non-smooth functions. Mathematical programming 103 (1), 127-152.
227. Nocedal, J., Wright, S., 2006. Numerical Optimization, Second Edition. Springer.
228. Nowak, R., Figueiredo, M., 2001. Fast wavelet-based image deconvolution using the EM algorithm. In: Proc. 35th Asilomar Conf. on Signals, Systems, and Computers. Vol. 1. pp. 371-375.
229. Nyquist, H., 1928. Certain topics in telegraph transmission theory. Transactions of the AIEE 47, 617-644.
230. Obozinski, G., Jacob, L., Vert, J.-P., 2011. Group Lasso with overlaps: The latent group Lasso approach. Tech. Rep. 1110.0413, arXiv.
231. Obozinski, G., Taskar, B., Jordan, M., 2010. Joint covariate selection and joint subspace selection for multiple classification problems. Statistics and Computing 20 (2), 231-252.
232. Olsen, P. A., Öztoprak, F., Nocedal, J., Rennie, S., 2012. Newton-like methods for sparse inverse covariance estimation. In: Proc. of Neural Information Processing Systems (NIPS). pp. 764-772.
233. Olshausen, B., Field, D., 1996. Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature 381 (6583), 607-609.
234. Olshausen, B., Field, D., 1997. Sparse coding with an overcomplete basis set: A strategy employed by V1? Vision Research 37, 3311-3325.
235. Osborne, M., Presnell, B., Turlach, B., 2000a. A new approach to variable selection in least squares problems. IMA Journal of Numerical Analysis 20 (3), 389-403.
236. Osborne, M., Presnell, B., Turlach, B., 2000b. On the Lasso and its dual. Journal of Computational and Graphical Statistics 9 (2), 319-337.
237. Park, M., Hastie, T., 2007. An l1 regularization-path algorithm for generalized linear models. JRSSB 69 (4), 659-677.
238. Patel, V., Chellappa, R., 2013. Sparse Representations and Compressive Sensing for Imaging and Vision. Springer Briefs in Electrical and Computer Engineering.
239. Pati, Y., Rezaiifar, R., Krishnaprasad, P., November 1993. Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition. In: Proc. 27th Annu. Asilomar Conf. Signals, Systems, and Computers. Vol. 1. pp. 40-44.
240. Pearl, J., 1988. Probabilistic reasoning in intelligent systems: Networks of plausible inference. Morgan Kaufmann, San Mateo, California.
241. Pearl, J., 2000. Causality: Models, Reasoning and Inference. Cambridge University Press.
242. Pearl, J., Paz, A., 1987. Graphoids: A graph based logic for reasoning about relevance relations. Advances in Artificial Intelligence II, 357-363.
243. Pearson, K., 1901. On lines and planes of closest fit to systems of points in space. Philosophical Magazine 2 (11), 559-572.
244. Pittsburgh EBC Group, 2007. PBAIC Homepage: http://www.ebc.pitt.edu/2007/competition.html.
245. Preston, C. J., 1973. Generalized Gibbs states and Markov random fields. Advances in Applied Probability 5 (2), 242-261.
246. 1,∞ regularization. In: Proc. of the 26th Annual International Conference on Machine Learning (ICML). pp. 857-864.
247. Rauhut, H., 2008. Stability results for random sampling of sparse trigonometric polynomials. IEEE Transactions on Information Theory 54 (12), 5661-5670.
248. 1-regularized MLE. In: Proc. of Neural Information Processing Systems (NIPS). pp. 1329-1336.
249. 1-regularized logistic regression. Ann. Statist. 38, 1287-1319.
250. Recht, B., Fazel, M., Parrilo, P., 2010. Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Review 52 (3), 471-501.
251. Resources, C. S., 2010. http://dsp.rice.edu/cs.
252. Rish, I., Brodie, M., Ma, S., Odintsova, N., Beygelzimer, A., Grabarnik, G., Hernandez, K., 2005. Adaptive diagnosis in distributed systems. IEEE Transactions on Neural Networks (special issue on Adaptive Learning Systems in Communication Networks) 16 (5), 1088-1109.
253. Rish, I., Cecchi, G., Baliki, M., Apkarian, A., 2010. Sparse regression models of pain perception. In: Brain Informatics. Springer, pp. 212-223.
254. Rish, I., Cecchi, G., Thyreau, B., Thirion, B., Plaze, M., Paillere-Martinot, M., Martelli, C., Martinot, J.L., Poline, J.B. 2013. Schizophrenia as a network disease: Disruption of emergent brain function in patients with auditory hallucinations. PLoS ONE 8 (1).
255. Rish, I., Cecchi, G. A., Heuton, K., February 2012a. Schizophrenia classification using fMRI-based functional network features. In: Proc. of SPIE Medical Imaging.
256. Rish, I., Cecchi, G. A., Heuton, K., Baliki, M. N., Apkarian, A. V., February 2012b. Sparse regression analysis of task-relevant information distribution in the brain. In: Proc. of SPIE Medical Imaging.
257. Rish, I., Grabarnik, G., 2009. Sparse signal recovery with exponential-family noise. In: Proc. of the 47th Annual Allerton Conference on Communication, Control, and Computing. pp. 60-66.
258. Rish, I., Grabarnik, G., Cecchi, G., Pereira, F., Gordon, G., 2008. Closed-form supervised dimensionality reduction with generalized linear models. In: Proc. of the 25th International Conference on Machine Learning (ICML). ACM, pp. 832-839.
259. Ritov, Y., December 2007. Discussion: The Dantzig selector: Statistical estimation when p is much larger than n. The Annals of Statistics 35 (6), 2370-2372.
260. Robertson, H., 1940. Communicated by s. goldstein received 15 november 1939 the statistical theory of isotropic turbulence, initiated by taylor (3) and extended by de karman and howarth (2), has proved of value in attacking problems. In: Proceedings of the Cambridge Philosophical Society: Mathematical and Physical Sciences. Vol. 36. Cambridge University Press, p. 209.
261. Rockafeller, R., 1970. Convex Analysis. Princeton University Press.
262. Rohde, A., Tsybakov, A., April 2011. Estimation of high-dimensional low-rank matrices. The Annals of Statistics 39 (2), 887-930.
263. Rosset, S., Zhu, J., 2007. Piecewise linear regularized solution paths. Annals of Statistics 35 (3).
264. Roth, V., Fischer, B., 2008. The group Lasso for generalized linear models: Uniqueness of solutions and efficient algorithms. In: Proc. of the 25th International Conference on Machine learning (ICML). pp. 848-855.
265. Rothman, A., Bickel, P., Levina, E., Zhu, J., 2008. Sparse permutation invariant covariance estimation. Electronic Journal of Statistics 2, 494-515.
266. Rudelson, M., 1999. Random vectors in the isotropic position. Journal of Functional Analysis 164 (1), 60-72.
267. Rudelson, M., 2007. Probabilistic and combinatorial methods in analysis, cbms lecture notes, preprint.
268. Rudelson, M., Vershynin, R., 2006. Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements. In: Proc. of the 40th Annual Conference on Information Sciences and Systems. pp. 207-212.
269. Rudelson, M., Vershynin, R., 2008. On sparse reconstruction from Fourier and Gaussian measurements. Communications on Pure and Applied Mathematics 61 (8), 1025-1045.
270. Rudin, L., Osher, S., Fatemi, E., 1992. Nonlinear total variation based noise removal algorithms. Physica D 60, 259-268.
271. Sajama, S., Orlitsky, A., 2004. Semi-parametric exponential family PCA. In: Proc. of Neural Information Processing Systems (NIPS). pp. 1177-1184.
272. Santosa, F., Symes, W., 1986. Linear inversion of band-limited reflection seismo-grams. SIAM Journal on Scientific and Statistical Computing 7 (4), 1307-1330.
273. Scheinberg, K., Asadi, N. B., Rish, I., 2009. Sparse MRF learning with priors on regularization parameters. Tech. Rep. RC24812, IBM T.J. Watson Research Center.
274. Scheinberg, K., Ma, S., 2011. Optimization methods for sparse inverse covariance selection. In: Sra, S., Nowozin, S., Wright, S. J. (Eds.), Optimization for Machine Learning. MIT Press.
275. Scheinberg, K., Ma, S., Goldfarb, D., 2010a. Sparse inverse covariance selection via alternating linearization methods. In: Proc. of Neural Information Processing Systems (NIPS). pp. 2101-2109.
276. Scheinberg, K., Rish, I., 2010. Learning sparse Gaussian Markov networks using a greedy coordinate ascent approach. In: Machine Learning and Knowledge Discovery in Databases. Springer, pp. 196-212.
277. Scheinberg, K., Rish, I., Asadi, N. B., January 2010b. Sparse Markov net learning with priors on regularization parameters. In: Proc. of International Symposium on AI and Mathematics (AIMATH 2010).
278. Schmidt, M., 2010. Graphical Model Structure Learning using L1-Regularization. Ph.D. thesis, University of British Columbia.
279. Schmidt, M., Berg, E. V. D., Friedl, M., Murphy, K., 2009. Optimizing costly functions with simple constraints: A limited-memory projected quasi-Newton algorithm. In: Proc. of the International Conference on Artificial Intelligence and Statistics (AISTATS). pp. 456-463.
280. Schmidt, M., Murphy, K., 2010. Convex structure learning in log-linear models: Beyond pairwise potentials. In: Proc. of the International Conference on Artificial Intelligence and Statistics (AISTATS). pp. 709-716.
281. 1-regularization paths. In: Proc. of the International Conference on Artificial Intelligence (AAAI). Vol. 7. pp. 1278-1283.
282. Schmidt, M., Rosales, R., Murphy, K., Fung, G., 2008. Structure learning in random fields for heart motion abnormality detection. In: Proc. of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, pp. 1-8.
283. Schrijver, A., 1986. Theory of linear and integer programming. John Wiley & Sons, Inc., New York, NY, USA.
284. Shannon, C. E., January 1949. Communication in the presence of noise. Proc. Institute of Radio Engineers 37 (1), 10-21.
285. Shashua, A., Hazan, T., 2005. Non-negative tensor factorization with applications to statistics and computer vision. In: Proc. of the 22nd International Conference on Machine Learning (ICML). ACM, pp. 792-799.
286. Shawe-Taylor, J., Cristianini, N., 2004. Kernel Methods for Pattern Analysis. Cambridge University Press.
287. Shelton, J., Sterne, P., Bornschein, J., Sheikh, A.-S., Lücke, J., 2012. Why MCA? Nonlinear sparse coding with spike-and-slab prior for neurally plausible image encoding. In: Proc. of Neural Information Processing Systems (NIPS). pp. 2285- 2293.
288. Shepp, L., Logan, B., 1974. The fourier reconstruction of a head section. IEEE Transactions on Nuclear Science 21 (3), 21-43.
289. Sherman, S., 1973. Markov random fields and Gibbs random fields. Israel Journal of Mathematics 14 (1), 92-103.
290. Sjöstrand, K. 2005. Matlab implementation of LASSO, LARS, the elastic net and SPCA: http://www2.imm.dtu.dk/pubdb/views/publicationdetails.php?id=3897.
291. Skretting, K., Engan, K., 2010. Recursive least squares dictionary learning algorithm. IEEE Transactions on Signal Processing 58 (4), 2121-2130.
292. Srebro, N., Rennie, J., Jaakkola, T., 2004. Maximum-margin matrix factorization. In: Proc. of Neural Information Processing Systems (NIPS). Vol. 17. pp. 1329-1336.
293. Starck, J.-L., Donoho, D., Candès, E., 2003a. Astronomical image representation by the curvelet transform. Astronomy and Astrophysics 398 (2), 785-800.
294. Starck, J.-L., Nguyen, M., Murtagh, F., 2003b. Wavelets and curvelets for image deconvolution: A combined approach. Signal Processing 83, 2279-2283.
295. Strohmer, T., Heath, R., 2003. Grassmannian frames with applications to coding and communication. Applied and Computational Harmonic Analysis 14 (3), 257-275.
296. Sun, L., Patel, R., Liu, J., Chen, K., Wu, T., Li, J., Reiman, E., Ye, J., 2009. Mining brain region connectivity for Alzheimer’s disease study via sparse inverse covariance estimation. In: Proc. of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD). ACM, pp. 1335-1344.
297. Szlam, A., Gregor, K., Cun, Y., 2011. Structured sparse coding via lateral inhibition. In: Proc. of Neural Information Processing Systems (NIPS). pp. 1116-1124.
298. Talagrand, M., 1996. Majorizing measures: The generic chaining. The Annals of Probability 24 (3), 1049-1103.
299. Tibshirani, R., 1996. Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society, Series B 58 (1), 267-288.
300. Tibshirani, R., 2013. The Lasso problem and uniqueness. Electronic Journal of Statistics 7, 1456-1490.
301. Tibshirani, R., Saunders, M., Rosset, S., Zhu, J., Knight, K., 2005. Sparsity and smoothness via the fused Lasso. Journal of the Royal Statistical Society Series B, 91-108.
302. Tibshirani, R., Wang, P., 2008. Spatial smoothing and hot spot detection for CGH data using the fused Lasso. Biostatistics 9 (1), 18-29.
303. Tipping, M., 2001. Sparse Bayesian learning and the Relevance Vector Machine. Journal of Machine Learning Research 1, 211-244.
304. Tipping, M., Bishop, C., 1999. Probabilistic principal component analysis. Journal of the Royal Statistical Society, Series B 21 (3), 611-622.
305. Toh, K.-C., Yun, S., 2010. An accelerated proximal gradient algorithm for nuclear norm regularized least squares problems. Pacific J. Optim. 6, 615-640.
306. Tosic, I., Frossard, P., 2011. Dictionary learning: What is the right representation for my signal? IEEE Signal Proc. Magazine 28 (2), 27-38.
307. Tropp, A., 2006. Just relax: Convex programming methods for subset slection and sparse approximation. IEEE Trans. Inform. Theory 51 (3), 1030-1051.
308. Tseng, P., Yun, S., 2009. A coordinate gradient descent method for nonsmooth separable minimization. Mathematical Programming 117 (1), 387-423.
309. Turlach, B., Venables, W., Wright, S., 2005. Simultaneous variable selection. Technometrics 47 (3), 349-363.
310. van de Geer, S., 2008. High-dimensional generalized linear models and the Lasso. Ann. Statist. 36, 614-645.
311. Vandenberghe, L., Boyd, S., Wu, S., 1998. Determinant maximization with linear matrix inequality constraints. SIAM J. Matrix Anal. Appl. 19 (2), 499-533.
312. Vardi, Y., 1996. Network tomography: Estimating source-destination traffic intensities from link data. J. Amer. Statist. Assoc. 91, 365-377.
313. Vershynin, R., 2012. Introduction to the non-asymptotic analysis of random matrices. In: Eldar, Y., Kutyniok, G. (Eds.), Compressed Sensing, Theory and Application. Cambridge University Press, pp. 210-268.
314. 1-constrained quadratic programming (Lasso). IEEE Transactions on Information Theory 55, 2183-2202.
315. 1-regularized logistic regression. Proc. of Neural Information Processing Systems (NIPS) 19, 1465-1472.
316. Weisberg, S., 1980. Applied Linear Regression. Wiley, New York.
317. Welch, L., 1974. Lower bounds on the maximum cross correlation of signals (cor-resp.). IEEE Transactions on Information Theory 20 (3), 397-399.
318. Whittaker, E., 1915. On the functions which are represented by the expansion of interpolating theory. Proc. R. Soc. Edinburgh 35, 181-194.
319. Whittaker, J., 1929. The Fourier theory of the cardinal functions. Proc. Math. Soc. Edinburgh 1, 169-176.
320. Whittaker, J., 1990. Graphical Models in Applied Multivariate Statistics. Wiley.
321. Wipf, D., Rao, B., August 2004. Sparse Bayesian learning for basis selection. IEEE Transactions on Signal Processing 52 (8), 2153-2164.
322. Witten, D., Tibshirani, R., Hastie, T., 2009. A penalized matrix decomposition, with applications to sparse canonical correlation analysis and principal components. Biostatistics 10 (3), 515-534.
323. Xiang, J., Kim, S., 2013. A* Lasso for learning a sparse Bayesian network structure for continuous variables. In: Proceedings of Neural Information Processing Systems (NIPS). pp. 2418-2426.
324. Xiang, Z., Xu, H., Ramadge, P., 2011. Learning sparse representations of high dimensional data on large scale dictionaries. In: Proc. of Neural Information Processing Systems (NIPS). Vol. 24. pp. 900-908.
325. Xu, W., Liu, X., Gong, Y., 2003. Document clustering based on non-negative matrix factorization. In: Proc. of the 26th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval. SIGIR ’03. ACM, pp. 267-273.
326. Yaghoobi, M., Blumensath, T., Davies, M., 2009. Dictionary learning for sparse approximations with the majorization method. IEEE Transactions on Signal Processing 57 (6), 2178-2191.
327. Yuan, M., 2010. Sparse inverse covariance matrix estimation via linear programming. Journal of Machine Learning Research 11, 2261-2286.
328. Yuan, M., Ekici, A., Lu, Z., Monteiro, R., 2007. Dimension reduction and coefficient estimation in multivariate linear regression. Journal of the Royal Statistical Society. Series B (Methodological) 69 (3), 329-346.
329. Yuan, M., Lin, Y., 2006. Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society, Series B 68, 49-67.
330. Yuan, M., Lin, Y., 2007. Model selection and estimation in the Gaussian graphical model. Biometrika 94(1), 19-35.
331. Zhao, P., Rocha, G., Yu, B., 2009. Grouped and hierarchical model selection through composite absolute penalties. Annals of Statistics 37 (6A), 3468-3497.
332. Zhao, P., Yu, B., November 2006. On model selection consistency of Lasso. J. Machine Learning Research 7, 2541-2567.
333. Zhao, P., Yu, B., 2007. Stagewise Lasso. Journal of Machine Learning Research 8, 2701-2726.
334. Zheng, A., Rish, I., Beygelzimer, A., 2005. Efficient test selection in active diagnosis via entropy approximation. In: Proc. of the Twenty-First Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI). AUAI Press, Arlington, Virginia, pp. 675-682.
335. Zhou, M., Chen, H., Ren, L., Sapiro, G., Carin, L., Paisley, J., 2009. Non-parametric Bayesian dictionary learning for sparse image representations. In: Proc. of Neural Information Processing Systems (NIPS). pp. 2295-2303.
336. Zou, H., 2006. The adaptive Lasso and its oracle properties. Journal of the American Statistical Association 101 (476), 1418-1429.
337. Zou, H., Hastie, T., 2005. Regularization and variable selection via the Elastic Net. Journal of the Royal Statistical Society, Series B 67 (2), 301-320.
338. Zou, H., Hastie, T., Tibshirani, R., 2006. Sparse principal component analysis. Journal of Computational and Graphical Statistics 15 (2), 262-286.