Alleviating label switching with optimal transport

Pierre Monteiller, Sebastian Claici, Edward Chien, Farzaneh Mirzazadeh, Justin Solomon, Mikhail Yurochkin

Research output: Contribution to journalConference articlepeer-review

4 Scopus citations


Label switching is a phenomenon arising in mixture model posterior inference that prevents one from meaningfully assessing posterior statistics using standard Monte Carlo procedures. This issue arises due to invariance of the posterior under actions of a group; for example, permuting the ordering of mixture components has no effect on the likelihood. We propose a resolution to label switching that leverages machinery from optimal transport. Our algorithm efficiently computes posterior statistics in the quotient space of the symmetry group. We give conditions under which there is a meaningful solution to label switching and demonstrate advantages over alternative approaches on simulated and real data.

Original languageEnglish
JournalAdvances in Neural Information Processing Systems
StatePublished - 2019
Externally publishedYes
Event33rd Annual Conference on Neural Information Processing Systems, NeurIPS 2019 - Vancouver, Canada
Duration: 8 Dec 201914 Dec 2019

Bibliographical note

Publisher Copyright:
© 2019 Neural information processing systems foundation. All rights reserved.


Acknowledgements. J. Solomon acknowledges the generous support of Army Research Office grant W911NF1710068, Air Force Office of Scientific Research award FA9550-19-1-031, of National Science Foundation grant IIS-1838071, from an Amazon Research Award, from the MIT-IBM Watson AI Laboratory, from the Toyota-CSAIL Joint Research Center, from the QCRI–CSAIL Computer Science Research Program, and from a gift from Adobe Systems. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of these organizations.

FundersFunder number
Toyota-CSAIL Joint Research Center
National Science FoundationIIS-1838071
Air Force Office of Scientific ResearchFA9550-19-1-031
Army Research OfficeW911NF1710068


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