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Alleviating Label Switching with Optimal Transport
Pierre Monteiller · Sebastian Claici · Edward Chien · Farzaneh Mirzazadeh · Justin Solomon · Mikhail Yurochkin

Thu Dec 12 10:45 AM -- 12:45 PM (PST) @ East Exhibition Hall B + C #206

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.

Author Information

Pierre Monteiller (ENS Ulm)
Sebastian Claici (MIT)
Edward Chien (Massachusetts Institute of Technology)
Farzaneh Mirzazadeh (MIT IBM Watson AI Lab)
Justin Solomon (MIT)
Mikhail Yurochkin (IBM Research, MIT-IBM Watson AI Lab)

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