PreprintarXiv licencearXiv
High-accuracy simulation of Picard HMC, part I: Gaussian cloud correction
Abstract
We study the problem of sampling from a continuous density π∝ exp(−V) on ℝd, where V∈ C2(ℝd) has a β-Lipschitz gradient and π satisfies a logarithmic Sobolev inequality with constant α−1, and write κ= β/α. We introduce the Gaussian cloud sampler, which achieves total variation accuracy ε using Õ(κd1/5 polylog(1/ε)) gradient queries in expectation. The algorithm uses first-order rejection sampling (FORS) to correct the law of smoothed Picard HMC trajectories. To do so, we represent the iterates of the ideal Picard iteration via Gaussian clouds, whose centers are never evaluated, and we develop a suite of likelihood correction gadgets which only use samples from this indirect cloud representation.
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BibTeX
@misc{chen2026highaccuracy,
title = {{High-accuracy simulation of Picard HMC, part I: Gaussian cloud correction}},
author = {Fan Chen and Sinho Chewi and Jianfeng Lu and Matthew S. Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38710},
eprint = {2609.38710},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38710},
}
RIS
TY - UNPB
TI - High-accuracy simulation of Picard HMC, part I: Gaussian cloud correction
AU - Fan Chen
AU - Sinho Chewi
AU - Jianfeng Lu
AU - Matthew S. Zhang
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.38710
UR - https://arxiv.org/abs/2609.38710
AB - We study the problem of sampling from a continuous density π∝ exp(−V) on ℝ^d, where V∈ C^2(ℝ^d) has a β-Lipschitz gradient and π satisfies a logarithmic Sobolev inequality with constant α^−1, and write κ= β/α. We introduce the Gaussian cloud sampler, which achieves total variation accuracy ε using Õ(κd^1/5 polylog(1/ε)) gradient queries in expectation. The algorithm uses first-order rejection sampling (FORS) to correct the law of smoothed Picard HMC trajectories. To do so, we represent the iterates of the ideal Picard iteration via Gaussian clouds, whose centers are never evaluated, and we develop a suite of likelihood correction gadgets which only use samples from this indirect cloud representation.
ER -