arXiv Machine Learning
Aug 3
Provable Diffusion Posterior Sampling for Bayesian Inversion
arXiv:2512. 08022v2 Announce Type: replace-cross Abstract: We propose a novel diffusion-based posterior sampling method within a plug-and-play framework.
Kinetic Interacting Particle Langevin Monte Carlo
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arXiv Machine Learning
Aug 7
The Tamed Subgradient Unadjusted Langevin Algorithm beyond Convexity
arXiv:2608. 06283v1 Announce Type: new Abstract: We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex.
arXiv Machine Learning
Jul 15
Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamics
arXiv:2510. 12311v2 Announce Type: replace-cross Abstract: We develop interacting particle algorithms for learning latent variable models with energy-based priors.
arXiv Machine Learning
Oct 8
Reflected Anchored Langevin Algorithms
The paper introduces Reflected Anchored Langevin Dynamics (RALD), a reflected diffusion that can converge to non‑differentiable target distributions on constrained domains. By employing a smooth anchored reference potential and scaling the drift and noise covariance with a state‑dependent factor, the authors derive an Euler‑Maruyama discretization with projection, yielding the Reflected Anchored Langevin Monte Carlo (RALMC) algorithm. Explicit convergence bounds and iteration complexity in the 2‑Wasserstein distance are proven, and numerical experiments confirm the theoretical predictions and empirical performance.
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.
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.
arXiv Machine Learning
Oct 23
Dimension-free regimes for unadjusted Langevin in ridge-separable models: A subspace robust Wasserstein analysis
arXiv:2610. 31431v1 Announce Type: cross Abstract: The Unadjusted Langevin Algorithm (ULA) is widely used for high-dimensional Bayesian inference.
Hugging Face Trending Papers
Oct 7
Reflected Anchored Langevin Algorithms
First order Langevin algorithms for constrained sampling in machine learning, such as projected Langevin Monte Carlo which are based on discretizations of reflected Langevin dynamics, require differen...
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.
arXiv Machine Learning
Oct 8
Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors
The paper introduces RED-KLwSGS, a new posterior sampling method for Bayesian imaging inverse problems that combines exact Gaussian updates for the data variable with underdamped (kinetic) Langevin diffusion for the auxiliary variable, driven by a one‑shot denoising score. It achieves the same per‑iteration cost as existing Langevin‑within‑SGS samplers while providing non‑asymptotic Wasserstein‑2 convergence guarantees for strongly log‑concave priors. A further variant, Joint-RED-KLwSGS, applies kinetic Langevin diffusion to both variables, and experiments using denoising diffusion probabilistic models on FFHQ and ImageNet demonstrate faster convergence and high‑quality image reconstruction.
arXiv Machine Learning
Jul 17
Delocalization of bias in unadjusted Hamiltonian Monte Carlo and underdamped Langevin
arXiv:2607. 15208v1 Announce Type: cross Abstract: Unadjusted samplers such as unadjusted Hamiltonian Monte Carlo and underdamped Langevin are well-known to be biased.
arXiv Machine Learning
Jun 2
Large-scale Uncertainty Quantification for Latent Variable Models Using Subsampling Markov Chain Monte Carlo
arXiv:2606. 00309v1 Announce Type: new Abstract: Stochastic gradient Langevin dynamics combined with Gibbs updates (SGLD--Gibbs) provides a highly scalable approach to approximate Bayesian inference in latent variable models.