Folded Transport MCMC: Certifiable Quotient Posterior Computation for Symmetric Bayesian Models

arXiv:2606.04307v1 Announce Type: new Abstract: Bayesian models with finite symmetry - mixture models with exchangeable components, structural identification with closely-spaced modes - define posteriors that are invariant under a group of label permutations, creating redundant multimodality that degrades MCMC convergence diagnostics. We introduce Folded Transport MCMC (FolT-MCMC), which performs inference directly on the quotient posterior by constructing an independence sampler on the fundamental domain of the symmetry group. The quotient proposal is formed by symmetrising a learned normalising flow over the group orbits. We prove that the LCNF oscillation-based certification framework transfers to the quotient metric with a stabiliser-corrected ball-mass bound and improved covering radius, and that the quantile-core certified lower bound improves whenever the unfolded flow exhibits cross-mode proposal deficiency. On Gaussian mixtures (d = 2 - 20), label-switching targets (up to 24 equivalent modes), and a standard Bayesian three-component mixture posterior, the quantile-core certified improvement ratio ranges from 2x to 145x, with the folded certificate empirically nearly dimension-free. On real accelerometer data from a supertall building during Typhoon Mangkhut, FolT-MCMC yields a non-vacuous quantile-core certificate where the unfolded certificate is vacuous.

Abstract:Bayesian models with finite symmetry - mixture models with exchangeable components, structural identification with closely-spaced modes - define posteriors that are invariant under a group of label permutations, creating redundant multimodality that degrades MCMC convergence diagnostics. We introduce Folded Transport MCMC (FolT-MCMC), which performs inference directly on the quotient posterior by constructing an independence sampler on the fundamental domain of the symmetry group. The quotient proposal is formed by symmetrising a learned normalising flow over the group orbits. We prove that the LCNF oscillation-based certification framework transfers to the quotient metric with a stabiliser-corrected ball-mass bound and improved covering radius, and that the quantile-core certified lower bound improves whenever the unfolded flow exhibits cross-mode proposal deficiency. On Gaussian mixtures (d = 2 - 20), label-switching targets (up to 24 equivalent modes), and a standard Bayesian three-component mixture posterior, the quantile-core certified improvement ratio ranges from 2x to 145x, with the folded certificate empirically nearly dimension-free. On real accelerometer data from a supertall building during Typhoon Mangkhut, FolT-MCMC yields a non-vacuous quantile-core certificate where the unfolded certificate is vacuous.

48 pages (including supplementary material), 5 figures, 6 tables. Submitted to Journal of the Royal Statistical Society: Series B

Machine Learning (cs.LG); Computation (stat.CO); Methodology (stat.ME)

arXiv:2606.04307 [cs.LG]

(or arXiv:2606.04307v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.04307 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Folded Transport MCMC: Certifiable Quotient Posterior Computation for Symmetric Bayesian Models

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