Delocalization of bias in unadjusted Hamiltonian Monte Carlo and underdamped Langevin

arXiv:2607.15208 · stat.CO, cs.LG, math.PR, stat.ML · Submitted 2026-07-16 · Read on arXiv

Yifan Chen, Xiaoou Cheng, Jonathan Niles-Weed, Jonathan Weare

stat.CO, cs.LG, math.PR, stat.ML

Submitted: 2026-07-16

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Chebyshev Polynomials — 13× in this paper · explained in 2 episodes
• Composition — 11× in this paper · explained in 2 episodes
• Langevin Dynamics — 10× in this paper · explained in 3 episodes
• Sparsity — 10× in this paper · explained in 5 episodes
• Accuracy — 5× in this paper · explained in 1 episode
• Core — 3× in this paper · explained in 2 episodes
• Convergence Guarantees — 2× in this paper · explained in 3 episodes
• Non-asymptotic Analysis — 2× in this paper · explained in 2 episodes
• Wasserstein Distance — 2× in this paper · explained in 6 episodes
• Bayesian Statistics — 1× in this paper · explained in 2 episodes
• Computational Biology — 1× in this paper · explained in 2 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Error Decomposition — 1× in this paper · explained in 4 episodes
• Generalization — 1× in this paper · explained in 14 episodes
• Higher-order derivatives — 1× in this paper · explained in 2 episodes
• Kullback-Leibler (KL) Divergence — 1× in this paper · explained in 6 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Stochastic Dynamics — 1× in this paper · explained in 3 episodes
• Structural Properties — 1× in this paper · explained in 2 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes
• Uncertainty Quantification — 1× in this paper · explained in 9 episodes

Sources

• Tail-Sensitive KL and R'enyi Convergence of Unadjusted Hamiltonian Monte Carlo via One-Shot Couplings
• Second order quantitative bounds for unadjusted generalized Hamiltonian Monte Carlo
• Unbiased Kinetic Langevin Monte Carlo with Inexact Gradients
• When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?
• Stein's method for marginals on large graphical models
• A hierarchical entropy method for the delocalization of bias in high-dimensional Langevin Monte Carlo
• Metropolis Adjusted Langevin Trajectories: a robust alternative to Hamiltonian Monte Carlo
• Practical and Scalable Hamiltonian Monte Carlo Without the Metropolis Test
• Convergence of kinetic Langevin samplers for non-convex potentials
• Algorithmic warm starts for Hamiltonian Monte Carlo

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