Primal-Dual methods for sparse constrained matrix completion

Yu Xin, Tommi Jaakkola
Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, PMLR 22:1323-1331, 2012.

Abstract

We develop scalable algorithms for regular and non-negative matrix completion. In particular, we base the methods on trace-norm regularization that induces a low rank predicted matrix. The regularization problem is solved via a constraint generation method that explicitly maintains a sparse dual and the corresponding low rank primal solution. We provide a new dual block coordinate descent algorithm for solving the dual problem with a few spectral constraints. Empirical results illustrate the effectiveness of our method in comparison to recently proposed alternatives.

Cite this Paper

BibTeX
@InProceedings{pmlr-v22-xin12, title = {Primal-Dual methods for sparse constrained matrix completion}, author = {Xin, Yu and Jaakkola, Tommi}, booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics}, pages = {1323--1331}, year = {2012}, editor = {Lawrence, Neil D. and Girolami, Mark}, volume = {22}, series = {Proceedings of Machine Learning Research}, address = {La Palma, Canary Islands}, month = {21--23 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v22/xin12/xin12.pdf}, url = {https://proceedings.mlr.press/v22/xin12.html}, abstract = {We develop scalable algorithms for regular and non-negative matrix completion. In particular, we base the methods on trace-norm regularization that induces a low rank predicted matrix. The regularization problem is solved via a constraint generation method that explicitly maintains a sparse dual and the corresponding low rank primal solution. We provide a new dual block coordinate descent algorithm for solving the dual problem with a few spectral constraints. Empirical results illustrate the effectiveness of our method in comparison to recently proposed alternatives.} }
Endnote
%0 Conference Paper %T Primal-Dual methods for sparse constrained matrix completion %A Yu Xin %A Tommi Jaakkola %B Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2012 %E Neil D. Lawrence %E Mark Girolami %F pmlr-v22-xin12 %I PMLR %P 1323--1331 %U https://proceedings.mlr.press/v22/xin12.html %V 22 %X We develop scalable algorithms for regular and non-negative matrix completion. In particular, we base the methods on trace-norm regularization that induces a low rank predicted matrix. The regularization problem is solved via a constraint generation method that explicitly maintains a sparse dual and the corresponding low rank primal solution. We provide a new dual block coordinate descent algorithm for solving the dual problem with a few spectral constraints. Empirical results illustrate the effectiveness of our method in comparison to recently proposed alternatives.
RIS
TY - CPAPER TI - Primal-Dual methods for sparse constrained matrix completion AU - Yu Xin AU - Tommi Jaakkola BT - Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics DA - 2012/03/21 ED - Neil D. Lawrence ED - Mark Girolami ID - pmlr-v22-xin12 PB - PMLR DP - Proceedings of Machine Learning Research VL - 22 SP - 1323 EP - 1331 L1 - http://proceedings.mlr.press/v22/xin12/xin12.pdf UR - https://proceedings.mlr.press/v22/xin12.html AB - We develop scalable algorithms for regular and non-negative matrix completion. In particular, we base the methods on trace-norm regularization that induces a low rank predicted matrix. The regularization problem is solved via a constraint generation method that explicitly maintains a sparse dual and the corresponding low rank primal solution. We provide a new dual block coordinate descent algorithm for solving the dual problem with a few spectral constraints. Empirical results illustrate the effectiveness of our method in comparison to recently proposed alternatives. ER -
APA
Xin, Y. & Jaakkola, T.. (2012). Primal-Dual methods for sparse constrained matrix completion. Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 22:1323-1331 Available from https://proceedings.mlr.press/v22/xin12.html.

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