论文标题
通过多级蒙特卡洛抽样估算有效的证据估算
Efficient Debiased Evidence Estimation by Multilevel Monte Carlo Sampling
论文作者
论文摘要
在本文中，我们提出了一种基于多级蒙特卡洛（MLMC）方法的贝叶斯推断的新随机优化算法。在贝叶斯统计数据中，模型证据的有偏见估计值通常被用作随机目标，因为现有的辩论技术在计算上是昂贵的。为了克服这个问题，我们将MLMC采样技术应用于模型证据及其梯度的构建低变化无偏估计器。在理论分析中，我们表明，我们提出的MLMC估计器所需的计算成本以给定精度估算模型证据或梯度所需的计算成本是比以前已知的估计器小的数量级。与常规估计器相比，我们的数值实验证实了可观的计算节省。将我们的MLMC估计量与基于梯度的随机优化相结合，从而为贝叶斯统计模型提供了一种新的可扩展，高效，依据的推理算法。
In this paper, we propose a new stochastic optimization algorithm for Bayesian inference based on multilevel Monte Carlo (MLMC) methods. In Bayesian statistics, biased estimators of the model evidence have been often used as stochastic objectives because the existing debiasing techniques are computationally costly to apply. To overcome this issue, we apply an MLMC sampling technique to construct low-variance unbiased estimators both for the model evidence and its gradient. In the theoretical analysis, we show that the computational cost required for our proposed MLMC estimator to estimate the model evidence or its gradient with a given accuracy is an order of magnitude smaller than those of the previously known estimators. Our numerical experiments confirm considerable computational savings compared to the conventional estimators. Combining our MLMC estimator with gradient-based stochastic optimization results in a new scalable, efficient, debiased inference algorithm for Bayesian statistical models.
