Convex Perturbations for Scalable Semidefinite Programming

Brian Kulis, Suvrit Sra, Inderjit Dhillon
Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics, PMLR 5:296-303, 2009.

Abstract

Many important machine learning problems are modeled and solved via semidefinite programs; examples include metric learning, nonlinear embedding, and certain clustering problems. Often, off-the-shelf software is invoked for the associated optimization, which can be inappropriate due to excessive computational and storage requirements. In this paper, we introduce the use of convex perturbations for solving semidefinite programs (SDPs), and for a specific perturbation we derive an algorithm that has several advantages over existing techniques: a) it is simple, requiring only a few lines of Matlab, b) it is a first-order method, and thereby scalable, and c) it can easily exploit the structure of a given SDP (e.g., when the constraint matrices are low-rank, a situation common to several machine learning SDPs). A pleasant byproduct of our method is a fast, kernelized version of the large-margin nearest neighbor metric learning algorithm. We demonstrate that our algorithm is effective in finding fast approximations to large-scale SDPs arising in some machine learning applications.

Cite this Paper

BibTeX
@InProceedings{pmlr-v5-kulis09a, title = {Convex Perturbations for Scalable Semidefinite Programming}, author = {Kulis, Brian and Sra, Suvrit and Dhillon, Inderjit}, booktitle = {Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics}, pages = {296--303}, year = {2009}, editor = {van Dyk, David and Welling, Max}, volume = {5}, series = {Proceedings of Machine Learning Research}, address = {Hilton Clearwater Beach Resort, Clearwater Beach, Florida USA}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v5/kulis09a/kulis09a.pdf}, url = {https://proceedings.mlr.press/v5/kulis09a.html}, abstract = {Many important machine learning problems are modeled and solved via semidefinite programs; examples include metric learning, nonlinear embedding, and certain clustering problems. Often, off-the-shelf software is invoked for the associated optimization, which can be inappropriate due to excessive computational and storage requirements. In this paper, we introduce the use of convex perturbations for solving semidefinite programs (SDPs), and for a specific perturbation we derive an algorithm that has several advantages over existing techniques: a) it is simple, requiring only a few lines of Matlab, b) it is a first-order method, and thereby scalable, and c) it can easily exploit the structure of a given SDP (e.g., when the constraint matrices are low-rank, a situation common to several machine learning SDPs). A pleasant byproduct of our method is a fast, kernelized version of the large-margin nearest neighbor metric learning algorithm. We demonstrate that our algorithm is effective in finding fast approximations to large-scale SDPs arising in some machine learning applications.} }
Endnote
%0 Conference Paper %T Convex Perturbations for Scalable Semidefinite Programming %A Brian Kulis %A Suvrit Sra %A Inderjit Dhillon %B Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2009 %E David van Dyk %E Max Welling %F pmlr-v5-kulis09a %I PMLR %P 296--303 %U https://proceedings.mlr.press/v5/kulis09a.html %V 5 %X Many important machine learning problems are modeled and solved via semidefinite programs; examples include metric learning, nonlinear embedding, and certain clustering problems. Often, off-the-shelf software is invoked for the associated optimization, which can be inappropriate due to excessive computational and storage requirements. In this paper, we introduce the use of convex perturbations for solving semidefinite programs (SDPs), and for a specific perturbation we derive an algorithm that has several advantages over existing techniques: a) it is simple, requiring only a few lines of Matlab, b) it is a first-order method, and thereby scalable, and c) it can easily exploit the structure of a given SDP (e.g., when the constraint matrices are low-rank, a situation common to several machine learning SDPs). A pleasant byproduct of our method is a fast, kernelized version of the large-margin nearest neighbor metric learning algorithm. We demonstrate that our algorithm is effective in finding fast approximations to large-scale SDPs arising in some machine learning applications.
RIS
TY - CPAPER TI - Convex Perturbations for Scalable Semidefinite Programming AU - Brian Kulis AU - Suvrit Sra AU - Inderjit Dhillon BT - Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics DA - 2009/04/15 ED - David van Dyk ED - Max Welling ID - pmlr-v5-kulis09a PB - PMLR DP - Proceedings of Machine Learning Research VL - 5 SP - 296 EP - 303 L1 - http://proceedings.mlr.press/v5/kulis09a/kulis09a.pdf UR - https://proceedings.mlr.press/v5/kulis09a.html AB - Many important machine learning problems are modeled and solved via semidefinite programs; examples include metric learning, nonlinear embedding, and certain clustering problems. Often, off-the-shelf software is invoked for the associated optimization, which can be inappropriate due to excessive computational and storage requirements. In this paper, we introduce the use of convex perturbations for solving semidefinite programs (SDPs), and for a specific perturbation we derive an algorithm that has several advantages over existing techniques: a) it is simple, requiring only a few lines of Matlab, b) it is a first-order method, and thereby scalable, and c) it can easily exploit the structure of a given SDP (e.g., when the constraint matrices are low-rank, a situation common to several machine learning SDPs). A pleasant byproduct of our method is a fast, kernelized version of the large-margin nearest neighbor metric learning algorithm. We demonstrate that our algorithm is effective in finding fast approximations to large-scale SDPs arising in some machine learning applications. ER -
APA
Kulis, B., Sra, S. & Dhillon, I.. (2009). Convex Perturbations for Scalable Semidefinite Programming. Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 5:296-303 Available from https://proceedings.mlr.press/v5/kulis09a.html.

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