Kinetic Interacting Particle Langevin Monte Carlo
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arXiv:2512. 08022v2 Announce Type: replace-cross Abstract: We propose a novel diffusion-based posterior sampling method within a plug-and-play framework.
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:2510. 12311v2 Announce Type: replace-cross Abstract: We develop interacting particle algorithms for learning latent variable models with energy-based priors.
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.
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: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.