SIAM/ASA Journal on Uncertainty Quantification, Volume 9, Issue 2, Page 507-535, January 2021.
In this paper we propose a novel and practical variance reduction approach for additive functionals of dependent sequences. Our approach combines the use of control variates with the minimization of an empirical variance estimate. We analyze finite sample properties of the proposed method and derive finite-time bounds of the excess asymptotic variance to zero. We apply our methodology to stochastic gradient Markov chain Monte Carlo (SGMCMC) methods for Bayesian inference on large data sets and combine it with existing variance reduction methods for SGMCMC. We present empirical results carried out on a number of benchmark examples showing that our variance reduction method achieves significant improvement as compared to state-of-the-art methods at the expense of a moderate increase of computational overhead.

中文翻译：

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相依序列的方差减少及其在随机梯度MCMC中的应用

SIAM / ASA不确定性量化期刊，第9卷，第2期，第507-535页，2021年1月。
在本文中，我们提出了一种新颖且实用的方差减少方法，用于相关序列的加法功能。我们的方法将控制变量的使用与经验方差估计的最小化结合在一起。我们分析了所提出方法的有限样本性质，并将过量渐近方差的有限时间范围推导出零。我们将我们的方法应用于对大型数据集进行贝叶斯推断的随机梯度马尔可夫链蒙特卡洛（SGMCMC）方法，并将其与SGMCMC的现有方差减少方法结合起来。我们提供了一些基准示例的经验结果，这些结果表明，与现有技术相比，我们的方差减少方法实现了显着改进，但代价是适度增加了计算开销。