Alleviating Label Switching with Optimal Transport
This addresses a specific issue in Bayesian statistics for researchers dealing with mixture models, offering an incremental improvement over existing approaches.
The paper tackles the label switching problem in mixture model posterior inference by proposing a resolution using optimal transport, which efficiently computes posterior statistics in the quotient space and demonstrates advantages over alternative methods on simulated and real data.
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.