arXiv:2509. 26175v2 Announce Type: replace Abstract: The Metropolis-within-Gibbs (MwG) algorithm is a widely used Markov chain Monte Carlo method for sampling from high-dimensional distributions when exact conditional sampling is intractable.
arXiv:2506.19186v2 Announce Type: replace-cross Abstract: We study the importance-tempered random-walk Metropolis (RWM) algorithm on $\mathbb{R}^d$, which targets the tempered density $\pi_\beta(x) \...
arXiv:2609.06906v1 Announce Type: cross Abstract: We develop a new low-accuracy sampler, called \emph{smoothed Picard Hamiltonian Monte Carlo}, which combines Gaussian smoothing, Picard iteration, an...
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.
arXiv:2402. 11736v3 Announce Type: replace Abstract: Kernel herding belongs to a family of deterministic quadratures that seek to minimize the maximum mean discrepancy (MMD), that is, the worst-case integration error over a reproducing kernel Hilbert space (RKHS).
arXiv:2606. 09926v1 Announce Type: cross Abstract: Sampling from the sequence-level power distribution $p^\alpha$ elicits RL-level reasoning from base language models without any parameter updates, but the standard Metropolis--Hastings (MH), a Markov Chain Monte Carlo (MCMC) sampler, is both expensive and slow-mixing.
arXiv:2608. 02430v1 Announce Type: cross Abstract: We provide new estimates in Wasserstein distance for the asymptotic bias of the unadjusted Langevin algorithm, in the classical setting of log-smooth strongly log-concave measures.
arXiv:2605. 30722v2 Announce Type: replace Abstract: We propose CerT-MCMC, a framework that equips learned-transport Markov chain Monte Carlo with automatic, rigorous convergence certificates.
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.
Local geometric mixing localizes geometric mixing by requiring geometric convergence to equilibrium in total variation only over finitely many transitions. It accommodates local convergence rates and...
arXiv:2610. 12052v1 Announce Type: cross Abstract: Despite their empirical success, why diffusion models overcome the bottlenecks of classical score-based samplers remains unclear.
arXiv:2512. 24152v2 Announce Type: replace-cross Abstract: Sampling based on score diffusions has led to striking empirical results, and has attracted considerable attention from various research communities.
arXiv:2608. 25273v1 Announce Type: cross Abstract: We analyze exact-metric, Metropolis-adjusted Dikin walks by keeping the proposal determinant and reverse quadratic form together.