167 citations · 405 across the 19 of their papers we have counts for
4 papers · 1 filter
Pre-integration via Active Subspaces
Sifan Liu, Art B. Owen
Pre-integration is an extension of conditional Monte Carlo to quasi-Monte Carlo and randomized quasi-Monte Carlo. It can reduce but not increase the variance in Monte Carlo. For qu…
The nonzero gain coefficients of Sobol's sequences are always powers of two
Zexin Pan, Art B. Owen
When a plain Monte Carlo estimate on samples has variance , then scrambled digital nets attain a variance that is as . For finite and an adversa…
A strong law of large numbers for scrambled net integration
Art B. Owen, Daniel Rudolf
This article provides a strong law of large numbers for integration on digital nets randomized by a nested uniform scramble. The motivating problem is optimization over some variab…
Mean Dimension of Ridge Functions
Christopher R. Hoyt, Art B. Owen
We consider the mean dimension of some ridge functions of spherical Gaussian random vectors of dimension . If the ridge function is Lipschitz continuous, then the mean dimension…