Solution stability in linear programming relaxations: Graph partitioning and unsupervised learning

Sebastian Nowozin, Stefanie Jegelka

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

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.

Original languageEnglish
Title of host publicationProceedings of the 26th Annual International Conference on Machine Learning, ICML'09
DOIs
StatePublished - 2009
Externally publishedYes
Event26th Annual International Conference on Machine Learning, ICML'09 - Montreal, QC, Canada
Duration: 14 Jun 200918 Jun 2009

Publication series

NameACM International Conference Proceeding Series
Volume382

Conference

Conference26th Annual International Conference on Machine Learning, ICML'09
Country/TerritoryCanada
CityMontreal, QC
Period14/06/0918/06/09

Fingerprint

Dive into the research topics of 'Solution stability in linear programming relaxations: Graph partitioning and unsupervised learning'. Together they form a unique fingerprint.

Cite this