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 normalis
This research addresses a long-standing challenge in Bayesian statistics, accelerated by the increasing complexity and symmetry found in modern AI models and data, which current MCMC methods struggle to handle efficiently.
Improved MCMC convergence diagnostics and efficiency for symmetric Bayesian models will significantly enhance the reliability and interpretability of complex AI systems, particularly in areas like statistical inference and machine learning.
The ability to perform inference directly on the quotient posterior via Folded Transport MCMC (FolT-MCMC) means more robust and certifiable computational methods for AI systems dealing with inherent symmetries, leading to more trustworthy AI outputs.
- · AI/ML researchers
- · Developers of complex AI models
- · Industries relying on statistical inference
- · Inefficient MCMC methods
- · Systems with unaddressed label permutation issues
More accurate and efficient Bayesian inference for models with inherent symmetries.
Accelerated development and deployment of robust AI models across various applications, reducing current computational bottlenecks.
Increased trust and wider adoption of AI systems in sensitive domains due to enhanced certifiability and reliability of their underlying statistical processes.
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