Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is satisfied with high probability. This work describes an extension of such methods which supports adaptive sampling to satisfy general error criteria for functions of a common array of expectations. Although several functions involving multiple expectations are being evaluated, only one random sequence is required, albeit sometimes of larger dimension than the underlying randomness. These enhanced Monte Carlo and Quasi-Monte Carlo algorithms are implemented in the QMCPy Python package with support for economic and parallel function evaluation. We exemplify these capabilities on problems from machine learning and global sensitivity analysis.

翻译：蒙特卡洛和拟蒙特卡洛方法为逼近随机变量的期望值提供了一种便捷途径。现有算法能够自适应地对随机变量进行采样，直至用户定义的绝对误差容限以高概率得到满足。本研究描述了对这些方法的扩展，支持自适应采样以满足涉及多重期望共同数组的函数的通用误差准则。尽管需要评估涉及多个期望的若干函数，但只需一个随机序列，尽管其维度有时会高于底层随机的维度。这些增强型蒙特卡洛和拟蒙特卡洛算法已在QMCPy Python包中实现，并支持经济化与并行化的函数评估。我们通过机器学习与全局灵敏度分析中的问题示例了这些能力。