论文标题
有条件的准蒙特卡洛与有限的活动子空间
Conditional Quasi-Monte Carlo with Constrained Active Subspaces
论文作者
论文摘要
有条件的蒙特卡洛或前整合是在使用蒙特卡洛和Quasi-Monte Carlo（QMC）方法时降低差异和改善常规性的强大工具。要选择变量预先融合，必须同时考虑该变量的重要性和条件期望的障碍。对于高斯分布上的积分，任何线性组合的变量都可以预先集成。 Liu and Owen（2022）提议基于积分的主空间分解选择线性组合。但是，预先整合所选方向可能会棘手。在这项工作中，我们通过发现受约束的主动空间来解决此问题，以便可以轻松地进行预一体化。所提出的算法还为预集成功能提供了缩小尺寸的计算效率替代方案。该方法适用于计算融资，密度估计和计算化学的示例，并显示出比以前的方法更小的误差。
Conditional Monte Carlo or pre-integration is a powerful tool for reducing variance and improving the regularity of integrands when using Monte Carlo and quasi-Monte Carlo (QMC) methods. To select the variable to pre-integrate, one must consider both the variable's importance and the tractability of the conditional expectation. For integrals over a Gaussian distribution, any linear combination of variables can potentially be pre-integrated. Liu and Owen (2022) propose to select the linear combination based on an active subspace decomposition of the integrand. However, pre-integrating the selected direction might be intractable. In this work, we address this issue by finding the active subspace subject to constraints such that pre-integration can be easily carried out. The proposed algorithm also provides a computationally-efficient alternative to dimension reduction for pre-integrated functions. The method is applied to examples from computational finance, density estimation, and computational chemistry, and is shown to achieve smaller errors than previous methods.
