Alleviating Label Switching with Optimal Transport
Pierre Monteiller, Sebastian Claici, Edward Chien, Farzaneh Mirzazadeh, Justin M Solomon, Mikhail Yurochkin
Abstract
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.
BibTeX
@inproceedings{NEURIPS2019_c2ae5cb2,
author = {Monteiller, Pierre and Claici, Sebastian and Chien, Edward and Mirzazadeh, Farzaneh and Solomon, Justin M and Yurochkin, Mikhail},
booktitle = {Advances in Neural Information Processing Systems},
editor = {H. Wallach and H. Larochelle and A. Beygelzimer and F. d\textquotesingle Alch\'{e}-Buc and E. Fox and R. Garnett},
pages = {},
publisher = {Curran Associates, Inc.},
title = {Alleviating Label Switching with Optimal Transport},
url = {https://proceedings.neurips.cc/paper_files/paper/2019/file/c2ae5cb2426d96ed19a50b0b7d7c8e11-Paper.pdf},
volume = {32},
year = {2019}
}