arXiv：cs.LG· Siran Liu, Michalis Tisias, Petros Dellaportas·· 4 小时前
基于变量变换与方差缩减的采样器
Transformed Samplers with Variance Reduction
AI 导读
研究者提出一种通过学习变量变换扩展控制变量解法的方法：用正规化流等双射将一般目标分布映射到潜在空间，使其接近参考密度，从而把已知谱分解的Markov核与Poisson解迁移过来，在潜在空间运行采样器即可得到显式控制变量。该估计量在映射与目标满足温和尾部条件下保持一致性，从流中进行重要性采样是其极限情形。合成目标与真实后验上的实验将该方法与当前最优采样器和控制变量进行了对比。
正文
Abstract:Markov chain Monte Carlo (MCMC) methods are the standard tool for computing expectations under complex probability distributions. Control variates reduce the variance of the resulting estimates, but a good control variate requires solving the Poisson equation of the sampler, which rarely admits a closed-form solution. Exact solutions are available when the sampler's kernel has a known spectral decomposition on a simple reference density. In our work, we extend these solutions to general targets through a learned change of variables. A bijection, such as a normalizing flow, is trained so that the target becomes close to the reference in a latent space, and we show that Markov kernels and their Poisson solutions are transformed by any bijection. Running such samplers in the latent space then yields explicit control variates, and the estimator is consistent under mild tail conditions on the map and target. Importance sampling (IS) from the flow is the limiting case of the same construction and the control variates apply to it as well. Experiments on synthetic targets and real posteriors compare the procedure against state-of-the-art samplers and control variates.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG); Methodology (stat.ME) |
| Cite as: | arXiv:2610.10870 [stat.ML] |
| (or arXiv:2610.10870v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.10870 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Siran Liu [view email]
[v1]
Wed, 7 Oct 2026 20:16:18 UTC (231 KB)
来源：arXiv：cs.LG · arxiv.org