arXiv Machine Learning By Yu Wang, Jie Ding, Jonathan H. Huggins

Accurate Large-sample Uncertainty Quantification using Stochastic Gradient Markov Chain Monte Carlo

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arXiv:2606. 00293v1 Announce Type: new Abstract: Tuning algorithms such as stochastic gradient descent (SGD) and stochastic gradient Langevin dynamics (SGLD) for approximate sampling and uncertainty quantification remains challenging, particularly in the practically relevant settings when the batch size is large or the model is misspecified.

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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