提出新采样方法，解决混合模型中标签混乱问题，提升收敛判断准确性。
Folded Transport MCMC: Eliminating Label Switching by Sampling on a Fundamental Domain
- 在对称性空间中限制采样路径，只保留一个等价模式代表。
- 实验显示采样效率提升2至145倍，且收敛诊断更稳定。
- 适合需要可靠后验推断的混合模型研究者使用。
在贝叶斯混合模型及其他可交换分量模型中，后验分布对分量标签的置换具有不变性，导致存在m!个等价极值——即标签切换问题。标准MCMC方法要么在这些极值间混合适应性差，要么依赖事后重标，无法保证采样已收敛。本文提出折叠传输MCMC（FolT-MCMC），通过将马尔可夫链限制在基本域（有序或反射子空间）内，在采样前消除标签切换。该方法采用学习的归一化流，其密度在群轨道上对称化，确保在约简空间上正确采样。我们证明此构造保持可计算的收敛诊断（基于对数密度比的振荡），且当原空间流覆盖不足时，该诊断在基本域上更加敏锐。在高斯混合（d=2–20）、最多24个等价极值的标签切换目标、标准三组分贝叶斯混合后验及超高层建筑加速度真实数据上的实验表明，性能提升2至145倍，折叠诊断随维度变化稳定，而未折叠诊断则崩溃。
原文摘要 · Abstract (English)
In Bayesian mixture models and other exchangeable-component models, the posterior is invariant under permutation of component labels, creating m! equivalent modes-the label-switching problem. Standard MCMC methods either mix poorly across these modes or rely on post-hoc relabelling that cannot guarantee the sampler has converged. We propose Folded Transport MCMC (FolT-MCMC), which eliminates label switching before sampling by restricting the Markov chain to a fundamental domain-a sorted or reflected subspace containing exactly one representative from each symmetric mode. The proposal is a learned normalising flow whose density is symmetrised over the group orbits, ensuring correct targeting on the reduced space. We show that this construction preserves a computable convergence diagnostic based on the oscillation of the log-density ratio, and that the diagnostic becomes sharper on the fundamental domain whenever the original-space flow under-covers one or more symmetric modes. Experiments on Gaussian mixtures (d=2-20), label-switching targets (up to 24 equivalent modes), a standard Bayesian three-component mixture posterior, and real accelerometer data from a supertall building show improvement ratios of 2x to 145x, with the folded diagnostic stable across dimensions while the unfolded diagnostic collapses.
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