title: Correlation method for variance reduction of Monte Carlo integration in RS-HDMR.
abstract: The High Dimensional Model Representation (HDMR) technique is a procedure for efficiently representing high-dimensional functions. A practical form of the technique, RS-HDMR, is based on randomly sampling the overall function and utilizing orthonormal polynomial expansions. The determination of expansion coefficients employs Monte Carlo integration, which controls the accuracy of RS-HDMR expansions. In this article, a correlation method is used to reduce the Monte Carlo integration error. The determination of the expansion coefficients becomes an iteration procedure, and the resultant RS-HDMR expansion has much better accuracy than that achieved by direct Monte Carlo integration. For an illustration in four dimensions a few hundred random samples are sufficient to construct an RS-HDMR expansion by the correlation method with an accuracy comparable to that obtained by direct Monte Carlo integration with thousands of samples.
authors.affiliation: Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Genyuan
authors.initials: G
authors.lastname: Li
authors.forename: Herschel
authors.initials: H
authors.lastname: Rabitz
authors.forename: Sheng-Wei
authors.initials: SW
authors.lastname: Wang
authors.forename: Panos G
authors.initials: PG
authors.lastname: Georgopoulos