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Solution Stability in Linear Programming Relaxations: Graph Partitioning and Unsupervised Learning

2009

Conference Paper

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We propose a new method to quantify the solution stability of a large class of combinatorial optimization problems arising in machine learning. As practical example we apply the method to correlation clustering, clustering aggregation, modularity clustering, and relative performance significance clustering. Our method is extensively motivated by the idea of linear programming relaxations. We prove that when a relaxation is used to solve the original clustering problem, then the solution stability calculated by our method is conservative, that is, it never overestimates the solution stability of the true, unrelaxed problem. We also demonstrate how our method can be used to compute the entire path of optimal solutions as the optimization problem is increasingly perturbed. Experimentally, our method is shown to perform well on a number of benchmark problems.

Author(s): Nowozin, S. and Jegelka, S.
Book Title: ICML 2009
Journal: Proceedings of the 26th International Conference on Machine Learning (ICML 2009)
Pages: 769-776
Year: 2009
Month: June
Day: 0
Editors: Danyluk, A. , L. Bottou, M. Littman
Publisher: ACM Press

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

DOI: 10.1145/1553374.1553473
Event Name: 26th International Conference on Machine Learning
Event Place: Montreal, Canada

Address: New York, NY, USA
Digital: 0
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF
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BibTex

@inproceedings{5878,
  title = {Solution Stability in Linear Programming Relaxations: Graph Partitioning and Unsupervised Learning},
  author = {Nowozin, S. and Jegelka, S.},
  journal = {Proceedings of the 26th International Conference on Machine Learning (ICML 2009)},
  booktitle = {ICML 2009},
  pages = {769-776},
  editors = {Danyluk, A. , L. Bottou, M. Littman},
  publisher = {ACM Press},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {New York, NY, USA},
  month = jun,
  year = {2009},
  month_numeric = {6}
}