论文标题
通过随机优化的蒙特卡洛方法的可扩展控制变体
Scalable Control Variates for Monte Carlo Methods via Stochastic Optimization
论文作者
论文摘要
控制变体是降低蒙特卡洛估计器方差的完善工具。但是，对于包括高维和大型样本设置在内的大规模问题，它们的优势可以被大量的计算成本所胜过。本文考虑了基于Stein运算符的控制变体，其提供了一个框架，该框架涵盖并概括了使用多项式，内核和神经网络的现有方法。提出了一种基于最小化通过随机优化目标的学习策略，从而导致可扩展有效的控制变体。提出了新的理论结果，以洞悉可以实现的差异，并提供了经验评估，包括对贝叶斯推论的应用。
Control variates are a well-established tool to reduce the variance of Monte Carlo estimators. However, for large-scale problems including high-dimensional and large-sample settings, their advantages can be outweighed by a substantial computational cost. This paper considers control variates based on Stein operators, presenting a framework that encompasses and generalizes existing approaches that use polynomials, kernels and neural networks. A learning strategy based on minimising a variational objective through stochastic optimization is proposed, leading to scalable and effective control variates. Novel theoretical results are presented to provide insight into the variance reduction that can be achieved, and an empirical assessment, including applications to Bayesian inference, is provided in support.
