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

Nowozin, S., & Jegelka, S. (2009). Solution Stability in Linear Programming Relaxations: Graph Partitioning and Unsupervised Learning. In A. Danyluk, L. Bottou, & M. Littman (Eds.), ICML '09: Proceedings of the 26th Annual International Conference on Machine Learning (pp. 769-776). New York, NY, USA: ACM Press.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-C4A5-4 Version Permalink: https://hdl.handle.net/21.11116/0000-0002-F91E-5
Genre: Conference Paper

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https://dl.acm.org/citation.cfm?doid=1553374.1553473 (Publisher version)
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 Creators:
Nowozin, S1, 2, Author           
Jegelka, S1, 2, Author           
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: 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.

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 Dates: 2009-06
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: DOI: 10.1145/1553374.1553473
BibTex Citekey: 5878
 Degree: -

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Title: 26th International Conference on Machine Learning (ICML 2009)
Place of Event: Montreal, Canada
Start-/End Date: 2009-06-14 - 2009-06-18

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Title: ICML '09: Proceedings of the 26th Annual International Conference on Machine Learning
Source Genre: Proceedings
 Creator(s):
Danyluk, A, Editor
Bottou, L, Editor
Littman, M, Editor
Affiliations:
-
Publ. Info: New York, NY, USA : ACM Press
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 769 - 776 Identifier: ISBN: 978-1-60558-516-1

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Title: ACM International Conference Proceeding Series
Source Genre: Series
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Publ. Info: -
Pages: - Volume / Issue: 382 Sequence Number: - Start / End Page: - Identifier: -