← Back to all news
arXiv Machine Learning By Stefan Oberd\"orster

Local Geometric Mixing via Dobrushin Contraction with Applications to Diffusion Path Monte Carlo and the Proximal Sampler

Read the original on arXiv Machine Learning →

The paper introduces the concept of local geometric mixing, which focuses on geometric convergence to equilibrium in total variation over a finite number of transitions, thereby capturing rapid local equilibration even when global mixing is slow. It derives local geometric mixing bounds using Dobrushin contraction and applies these results to Diffusion Path Monte Carlo, a Markov chain Monte Carlo method that aligns with the Proximal Sampler. The analysis provides mixing guarantees for both the ideal method and its Metropolis-adjusted implementation, and extends recent spectral gap estimates into mixing time bounds.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

Related stories

arXiv Statistics ML
Sep 4

Markov Chain Monte Carlo with Diffusion Paths

The paper introduces a new Markov chain Monte Carlo method that samples from multimodal distributions by interpolating along the diffusion path of a noising diffusion process, preserving mode weights and improving mixing. It proposes a Metropolis-adjusted diffusion path (MAD-Path) sampler that corrects for bias from approximate score estimates and discretization errors, ensuring the target distribution remains invariant. Experiments on Bayesian posteriors demonstrate that MAD-Path outperforms tempering-based MCMC and unadjusted diffusion samplers in global exploration and accurate mode-weight estimation.

By Han Chen, Sifan Liu, Jun Yang
diffusionmultimodalsafety
More like this →
Hugging Face Trending Papers
Jul 8

Gradient-free Riemannian Langevin Sampler

We address the problem of efficiently sampling multimodal probability distributions, where standard Markov Chain Monte Carlo methods often suffer from poor mixing and mode trapping. To mitigate these issues, we propose Gradient-free Riemannian Langevin Sampler (GRiLS), a novel proposal that improves exploration without requiring gradient evaluations of the target density.

multimodalbenchmarks
More like this →