CONDITIONAL QUASI-MONTE CARLO WITH CONSTRAINED ACTIVE SUBSPACES

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 [SIAM J. Numer. Anal., 61 (2023), pp. 495-514] 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.

Duke Scholars

Author Sifan Liu Statistical Science