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

Abstract

Bayesian frameworks characterized by finite symmetry—such as mixture models featuring exchangeable components or structural identification scenarios involving closely spaced modes—generate posteriors that remain invariant under specific label permutation groups. This invariance introduces redundant multimodality, which subsequently impairs MCMC convergence diagnostics. To address this, we present Folded Transport MCMC (FolT-MCMC), a method that conducts inference directly on the quotient posterior. This approach constructs an independence sampler operating within the fundamental domain of the symmetry group. The resulting quotient proposal is derived by symmetrizing a learned normalizing flow across group orbits.

We demonstrate that the LCNF oscillation-based certification framework extends to the quotient metric, incorporating a stabiliser-corrected ball-mass bound and an enhanced covering radius. Furthermore, we show that the quantile-core certified lower bound sees improvement whenever the unfolded flow displays a deficiency in cross-mode proposal capability. Empirical evaluations on Gaussian mixtures (with dimensions d = 2–20), label-switching targets (featuring up to 24 equivalent modes), and a standard Bayesian three-component mixture posterior reveal that the quantile-core certified improvement ratio spans from 2x to 145x. Notably, the folded certificate appears to be nearly dimension-free. Additionally, analysis of real-world accelerometer data collected from a supertall building during Typhoon Mangkhut demonstrates that FolT-MCMC produces a non-vacuous quantile-core certificate, a feat achieved where the unfolded certificate fails and remains vacuous.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC