{"ID":3053297,"CreatedAt":"2026-06-04T04:41:36.695875263Z","UpdatedAt":"2026-06-06T00:15:09.974762002Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.04307","arxiv_id":"2606.04307","title":"Folded Transport MCMC: Certifiable Quotient Posterior Computation for Symmetric Bayesian Models","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.","short_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 M...","url_abs":"https://arxiv.org/abs/2606.04307","url_pdf":"https://arxiv.org/pdf/2606.04307v1","authors":"[\"Jun Hu\"]","published":"2026-06-03T00:26:46Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"stat.CO\",\"stat.ME\"]","methods":"[]","has_code":false}