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State transition algorithm
A proximal alternating direction method for $\ell_{2,1}$-norm least squares problem in multi-task feature learning
1. | Institute of Applied Mathematics, Henan University, Kaifeng 475004 |
2. | National Center for Theoretical Sciences (South), National Cheng Kung University, Tainan 700, Taiwan |
3. | Department of Mathematics, Nanjing University, Nanjing 210093, China |
References:
[1] |
R. K. Ando and T. Zhang, A framework for learning predictive structures from multiple tasks and unlabeleddata,, Journal of Machine Learning Research, 6 (2005), 1817.
|
[2] |
A. Argyriou, T. Evgeniou and M. Pontil, Convex multi-convex feature learning,, Machine Learning, 73 (2008), 243. Google Scholar |
[3] |
B. Bakker and T. Heskes, Task clustering and gating for Bayesian multi-task learning,, Journal of Machine Learning Research, 4 (2003), 83. Google Scholar |
[4] |
S. Chen, D. Donoho and M. Saunders, Atomic decomposition by basis pursuit,, SIAM Journal on Scientific Computing, 20 (1999), 33.
doi: 10.1137/S1064827596304010. |
[5] |
J. Duchi and Y. Singer, Efficient online and batch learning using forward backward splitting,, Journal of Machine Learning Research, 10 (2009), 2899.
|
[6] |
T. Evgeniou, C. A. Micchelli and M. Pontil, Learning multiple tasks with kernel methods,, Journal of Machine Learning Research, 6 (2005), 615.
|
[7] |
D. Gabay and B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite-element approximations,, Computers & Mathematics with Applications, 2 (1976), 17. Google Scholar |
[8] |
R. Glowinski, "Numerical Methods for Nonlinear Variational Problems,", Springer, (1984).
|
[9] |
R. Glowinski and A. Marrocco, Sur l'approximation, par élémentsfinis d'ordre un, et la résolution, parpénalisation-dualité d'une classe de problèmes deDirichlet nonlinéaires,, Revue Francaise d'automatique, 2 (1975), 41.
|
[10] |
B. He, L. Z. Liao, D. Han and H. Yang, A new inexact alternating directions method for monotone variational inequalities,, Mathematical Programming, 92 (2002), 103.
doi: 10.1007/s101070100280. |
[11] |
B. He, S. L. Wang and H. Yang, A modified variable-penalty alternating directions method for monotone variational inequalities,, Journal of Computational Mathematics, 21 (2003), 495.
|
[12] |
J. Liu, J. Chen and J. Ye, "Large-Scale Sparse Logistic Regression,", in, (2009). Google Scholar |
[13] |
J. Liu, S. Ji and J. Ye, "Multi-Task Feather Learning Via Efficient $l_{2,1}$-norm Minimization,", in, (2009). Google Scholar |
[14] |
M. Kowalski, Sparse regression using mixednorms,, Applied and Computational Harmonic Analysis, 27 (2009), 303.
doi: 10.1016/j.acha.2009.05.006. |
[15] |
M. Kowalski, M. Szafranski and L. Ralaivola, "Multiple Indefinite Kernel Learning with Mixed Normregularization,", Proceedings of the 26th Annual International Conference on Machine Learning, (2009). Google Scholar |
[16] |
A. Nemirovski, "Efficient Methods in Convex Programming,", Lecture Notes, (1994). Google Scholar |
[17] |
Y. Nesterov, "Introductory Lectures on Convex Optimization: A Basic Course,", Kluwer Academic Publishers, (2003).
|
[18] |
Y. Nesterov, "Gradient Methods for Minimizing Composite Objective Function,", CORE report, (2007). Google Scholar |
[19] |
F. Nie, H. Huang, X. Cai and C. Ding, "Efficient and Robust Feature Selection via Joint $l_{2,1}$-Normsminimization,", Neural Information Processing Systems Foundation, (2010). Google Scholar |
[20] |
G. Obozinski, B. Taskar and M. I. Jordan, "Multi-Task Feature Selection,", Technical Report, (2006). Google Scholar |
[21] |
Y. Saeys, I. Inza and P. Larranaga, A review of feature selection techniques in bioinformatics,, Bioinformatics, 23 (2007), 2507.
doi: 10.1093/bioinformatics/btm344. |
[22] |
Y. Xiao, S.-Y. Wu and D.-H. Li, Splitting and linearizing augmented Lagrangian algorithm for subspace recovery from corrupted observations,, Adv. Comput. Math., (): 10444. Google Scholar |
[23] |
T. Xiong, J. Bi, B. Rao and V. Cherkassky, "Probabilistic Joint Feature Selection for Multi-Task Learning,", in, (2006). Google Scholar |
[24] |
M. H. Xu, Proximal alternating directions method for structured variational inequalities,, Journal of Optimization Theory and Applications, 134 (2007), 107.
doi: 10.1007/s10957-007-9192-2. |
[25] |
J. Yang, Dynamic power price problem: An inverse variational inequality approach,, Journal of Industrial and Management Optimization, 4 (2008), 673.
|
[26] |
J. Yang and X. Yuan, Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization,, Math. Comput., ().
doi: 10.1090/S0025-5718-2012-02598-1. |
[27] |
J. Yang and Y. Zhang, Alternating direction algorithms for $l_1$-problemsin compressive sensing,, SIAM Journal on Scientific Computing, 33 (2011), 250.
doi: 10.1137/090777761. |
[28] |
J. Zhang, Z. Ghahramani and Y. Yang, Flexible latent variable models for multi-task learning,, Machine Learning, 73 (2008), 221. Google Scholar |
show all references
References:
[1] |
R. K. Ando and T. Zhang, A framework for learning predictive structures from multiple tasks and unlabeleddata,, Journal of Machine Learning Research, 6 (2005), 1817.
|
[2] |
A. Argyriou, T. Evgeniou and M. Pontil, Convex multi-convex feature learning,, Machine Learning, 73 (2008), 243. Google Scholar |
[3] |
B. Bakker and T. Heskes, Task clustering and gating for Bayesian multi-task learning,, Journal of Machine Learning Research, 4 (2003), 83. Google Scholar |
[4] |
S. Chen, D. Donoho and M. Saunders, Atomic decomposition by basis pursuit,, SIAM Journal on Scientific Computing, 20 (1999), 33.
doi: 10.1137/S1064827596304010. |
[5] |
J. Duchi and Y. Singer, Efficient online and batch learning using forward backward splitting,, Journal of Machine Learning Research, 10 (2009), 2899.
|
[6] |
T. Evgeniou, C. A. Micchelli and M. Pontil, Learning multiple tasks with kernel methods,, Journal of Machine Learning Research, 6 (2005), 615.
|
[7] |
D. Gabay and B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite-element approximations,, Computers & Mathematics with Applications, 2 (1976), 17. Google Scholar |
[8] |
R. Glowinski, "Numerical Methods for Nonlinear Variational Problems,", Springer, (1984).
|
[9] |
R. Glowinski and A. Marrocco, Sur l'approximation, par élémentsfinis d'ordre un, et la résolution, parpénalisation-dualité d'une classe de problèmes deDirichlet nonlinéaires,, Revue Francaise d'automatique, 2 (1975), 41.
|
[10] |
B. He, L. Z. Liao, D. Han and H. Yang, A new inexact alternating directions method for monotone variational inequalities,, Mathematical Programming, 92 (2002), 103.
doi: 10.1007/s101070100280. |
[11] |
B. He, S. L. Wang and H. Yang, A modified variable-penalty alternating directions method for monotone variational inequalities,, Journal of Computational Mathematics, 21 (2003), 495.
|
[12] |
J. Liu, J. Chen and J. Ye, "Large-Scale Sparse Logistic Regression,", in, (2009). Google Scholar |
[13] |
J. Liu, S. Ji and J. Ye, "Multi-Task Feather Learning Via Efficient $l_{2,1}$-norm Minimization,", in, (2009). Google Scholar |
[14] |
M. Kowalski, Sparse regression using mixednorms,, Applied and Computational Harmonic Analysis, 27 (2009), 303.
doi: 10.1016/j.acha.2009.05.006. |
[15] |
M. Kowalski, M. Szafranski and L. Ralaivola, "Multiple Indefinite Kernel Learning with Mixed Normregularization,", Proceedings of the 26th Annual International Conference on Machine Learning, (2009). Google Scholar |
[16] |
A. Nemirovski, "Efficient Methods in Convex Programming,", Lecture Notes, (1994). Google Scholar |
[17] |
Y. Nesterov, "Introductory Lectures on Convex Optimization: A Basic Course,", Kluwer Academic Publishers, (2003).
|
[18] |
Y. Nesterov, "Gradient Methods for Minimizing Composite Objective Function,", CORE report, (2007). Google Scholar |
[19] |
F. Nie, H. Huang, X. Cai and C. Ding, "Efficient and Robust Feature Selection via Joint $l_{2,1}$-Normsminimization,", Neural Information Processing Systems Foundation, (2010). Google Scholar |
[20] |
G. Obozinski, B. Taskar and M. I. Jordan, "Multi-Task Feature Selection,", Technical Report, (2006). Google Scholar |
[21] |
Y. Saeys, I. Inza and P. Larranaga, A review of feature selection techniques in bioinformatics,, Bioinformatics, 23 (2007), 2507.
doi: 10.1093/bioinformatics/btm344. |
[22] |
Y. Xiao, S.-Y. Wu and D.-H. Li, Splitting and linearizing augmented Lagrangian algorithm for subspace recovery from corrupted observations,, Adv. Comput. Math., (): 10444. Google Scholar |
[23] |
T. Xiong, J. Bi, B. Rao and V. Cherkassky, "Probabilistic Joint Feature Selection for Multi-Task Learning,", in, (2006). Google Scholar |
[24] |
M. H. Xu, Proximal alternating directions method for structured variational inequalities,, Journal of Optimization Theory and Applications, 134 (2007), 107.
doi: 10.1007/s10957-007-9192-2. |
[25] |
J. Yang, Dynamic power price problem: An inverse variational inequality approach,, Journal of Industrial and Management Optimization, 4 (2008), 673.
|
[26] |
J. Yang and X. Yuan, Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization,, Math. Comput., ().
doi: 10.1090/S0025-5718-2012-02598-1. |
[27] |
J. Yang and Y. Zhang, Alternating direction algorithms for $l_1$-problemsin compressive sensing,, SIAM Journal on Scientific Computing, 33 (2011), 250.
doi: 10.1137/090777761. |
[28] |
J. Zhang, Z. Ghahramani and Y. Yang, Flexible latent variable models for multi-task learning,, Machine Learning, 73 (2008), 221. Google Scholar |
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