Diffusive Gibbs Sampling
CoRR(2024)
摘要
The inadequate mixing of conventional Markov Chain Monte Carlo (MCMC) methods
for multi-modal distributions presents a significant challenge in practical
applications such as Bayesian inference and molecular dynamics. Addressing
this, we propose Diffusive Gibbs Sampling (DiGS), an innovative family of
sampling methods designed for effective sampling from distributions
characterized by distant and disconnected modes. DiGS integrates recent
developments in diffusion models, leveraging Gaussian convolution to create an
auxiliary noisy distribution that bridges isolated modes in the original space
and applying Gibbs sampling to alternately draw samples from both spaces. Our
approach exhibits a better mixing property for sampling multi-modal
distributions than state-of-the-art methods such as parallel tempering. We
demonstrate that our sampler attains substantially improved results across
various tasks, including mixtures of Gaussians, Bayesian neural networks and
molecular dynamics.
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