Self-Certifying Transport MCMC via Dual Spectral-Gap Certificates
Two new research papers introduce frameworks for certifying the convergence of Transport MCMC, a method that uses normalizing flows to improve Markov chain Monte Carlo sampling efficiency. The first paper, "Non-Vacuous Certification of Transport MCMC via Oscillation-Controlled Normalizing Flows," establishes rigorous spectral-gap bounds for these samplers, overcoming previous limitations in higher dimensions. The second paper, "Self-Certifying Transport MCMC via Dual Spectral-Gap Certificates," proposes a framework called CerT-MCMC with two complementary certificates that provide automatic, dimension-aware convergence guarantees, distinguishing true failures from proof limitations. AI
IMPACT Advances theoretical guarantees for sampling methods used in Bayesian inference and machine learning.