🤖 AI Summary
To address the susceptibility of Markov chain Monte Carlo (MCMC) algorithms to local optima within the approximate Bayesian computation (ABC) framework, this paper proposes a global-local adaptive hybrid sampling scheme. The method iteratively constructs a dynamic global proposal distribution via importance resampling, while enhancing local move efficiency through Langevin dynamics integrated with common random numbers. It introduces, for the first time, a regularization-based normalizing flow approach to learn the importance sampling distribution, enabling adaptive optimization of its shape. Furthermore, an expected squared jump distance (ESJD)-driven adaptive coordination strategy is designed to balance exploration and exploitation. Experiments demonstrate substantial improvements in sampling efficiency and convergence reliability for complex multimodal posterior distributions. The implementation is publicly available on GitHub.
📝 Abstract
In this paper, we address the challenge of Markov Chain Monte Carlo algorithms within the Approximate Bayesian Computation framework, which often get trapped in local optima due to their inherent local exploration mechanism. We propose a novel Global-Local ABC-MCMC algorithm that combines the"exploration"capabilities of global proposals with the"exploitation"finesse of local proposals. By integrating iterative importance resampling into the likelihood-free framework, we establish an effective global proposal distribution. We select the optimum mixture of global and local moves based on a unit cost version of expected squared jumped distance via sequential optimization. Furthermore, we propose two adaptive schemes: The first involves a normalizing flow-based probabilistic distribution learning model to iteratively improve the proposal for importance sampling, and the second focuses on optimizing the efficiency of the local sampler by utilizing Langevin dynamics and common random numbers. We numerically demonstrate that our method improves sampling efficiency and achieve more reliable convergence for complex posteriors. A software package implementing this method is available at https://github.com/caofff/GL-ABC-MCMC.