arXiv:2605.30722v1 Announce Type: new Abstract: We propose CerT-MCMC, a framework that equips learned-transport Markov chain Monte Carlo with automatic, rigorous convergence certificates. A normalising flow maps a Gaussian reference to an approximation of the target posterior; the same flow then serves as both the independence Metropolis-Hastings proposal and the basis for a computable spectral-gap bound. We develop two complementary certificates. The covering certificate bounds the weight-ratio oscillation over the full proposal support via finite-sample covering arguments, yielding full-supp
The continuous advancements in AI and machine learning necessitate more rigorous methods for model evaluation and reliability, particularly for complex probabilistic models.
This development addresses a critical need for explainable and certifiable AI, allowing for greater trust and broader application of sophisticated MCMC techniques in high-stakes domains.
The ability to automatically generate convergence certificates for MCMC models reduces the black-box nature of learned-transport methods, offering a transparent measure of their reliability.
- · AI researchers
- · Machine learning practitioners
- · High-stakes application sectors (e.g., finance, healthcare, defense)
- · Developers of uncertifiable or opaque probabilistic models
Increased adoption of certifiable AI methods in probabilistic modeling and sampling.
Reduced regulatory hurdles for AI systems that can demonstrate provable convergence and reliability.
Acceleration of research into self-certifying or provably robust AI algorithms across various subfields.
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Read at arXiv cs.LG