# Conditional Quasi-Monte Carlo with Constrained Active Subspaces

arXiv: https://arxiv.org/abs/2212.13232 · HTML: https://mlsanity.com/paper/2212.13232/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Dec 2022.

## Built on by (most cited first, 1 of 1)

- [Transport Quasi-Monte Carlo](https://mlsanity.com/paper/2412.16416/) (2024)

## Abstract (arXiv)

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.