← Back to all news
arXiv Statistics ML

A Non-asymptotic Analysis for Learning and Applying a Preconditioner in MCMC

The paper presents a non‑asymptotic analysis of Markov chain Monte Carlo (MCMC) algorithms that learn and apply a preconditioner based on either the target covariance or the expected Hessian of the target potential. It compares the finite‑time computational costs of these preconditioned schemes with unpreconditioned counterparts, providing guarantees for algorithms such as the Unadjusted Langevin Algorithm (ULA) and the proximal sampler. The analysis relies on a contraction assumption in the Wasserstein‑2 distance to formalize approximate independence and bridge modern MCMC theory with classical effective sample size heuristics.

Related stories

arXiv Machine Learning
Aug 27

Improved Analysis for Hessian-free High-resolution Monte Carlo Sampling

The paper introduces Hessian-free high-resolution (HFHR) dynamics, an extension of underdamped Langevin dynamics that incorporates reversible position diffusion for sampling in machine learning. It provides an explicit quantitative contraction rate under a position Poincaré inequality, weighted Hessian and Laplacian bounds, and a compact Sobolev embedding, even when the potential is non‑convex. For the HFHR Monte Carlo algorithm, a path‑space Girsanov argument yields a non‑asymptotic convergence bound and an explicit iteration complexity in total variation distance, improving on previous HFHR results and demonstrating benefits of a positive diffusion parameter through numerical experiments.

By Wujun Lv, Xiaoyu Wang, Yingli Wang, Lingjiong Zhu
ragdiffusion
More like this →
Hugging Face Trending Papers
Aug 6

The Tamed Subgradient Unadjusted Langevin Algorithm beyond Convexity

We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex. We introduce the Subgradient Tamed Unadjusted Langevin Algorithm (SG-TULA), a discretisation of the Langevin diffusion that operates directly on subgradients, without relying on computationally demanding smoothing procedures.

llmsdiffusion
More like this →
arXiv Statistics ML
Aug 25

Provably adaptive sampling with uniform and remasking discrete diffusion models

The paper proves that for discrete diffusion models using uniform or remasking forward processes, an adaptive sampler based on a leave‑one‑out denoiser can achieve sampling error proportional to the score‑estimation error plus a small tolerance. The required number of discretization steps scales with the dual total correlation of the target distribution, not directly with the ambient dimension. This result shows that sampling complexity is governed by the intrinsic dependence structure of the distribution, and the authors provide an information‑theoretic analysis linking discretization error to mutual information between coordinates.

By Daniil Dmitriev, Zhihan Huang, Yuting Wei
diffusion
More like this →
arXiv Machine Learning
Jun 17

Randomized Midpoint Method for Log-Concave Sampling under Constraints

arXiv:2405. 15379v3 Announce Type: replace-cross Abstract: In this paper, we study the problem of sampling from log-concave distributions supported on convex and compact sets, with a particular focus on the randomized midpoint discretization of both overdamped and kinetic Langevin diffusions in constrained domains.

By Yifeng Yu, Shijie Zhang, Lu Yu
diffusion
More like this →
arXiv Machine Learning
Jul 7

Non-Asymptotic Error Bounds for SMC with Biased Proposals: Application to Conditional Diffusion Sampling

arXiv:2607. 04780v1 Announce Type: cross Abstract: Sequential Monte Carlo (SMC) methods are a natural tool for post-hoc conditioning of pretrained generative models, but in many applications the mutation kernels used by the particle system are biased approximations of an ideal Feynman--Kac flow.

By Stanislas Strasman (SU, LPSM), Gabriel Victorino Cardoso (LPSM), Sylvain Le Corff (LPSM), Vincent Lemaire (LPSM), Antonio Ocello
diffusionsafety
More like this →