Lifting the Curse of Dimensionality

By Frances Y. Kuo, Ian H. Sloan. 2005

193 citations recorded by the source corpus.

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Citations in the corpus

Super-Samples from Kernel Herding (2010, methodology): “In fact, under the assumption that we perform an unweighed Monte Carlo sum,O(1/T ) convergence is known to be optimal [Kuo and Sloan, 2005].”
Improved Multilevel Monte Carlo Convergence using the Milstein Scheme (2008, methodology): “For these low dimensional levels it is reasonable to expect that quasi-Monte Carlo methods [10, 11] will be very much more effective than the standard Monte Carlo methods used in this paper.”
The Bayesian Approach to Inverse Problems (2013, background): “effectively in some such high dimensional integration problems; [59] and [77] are general references on the QMC methodology.”
Support points (2016, background): “Moreover, when p is allowed to vary, it can be shown (see [35, 11]) that certain randomized QMC (RQMC) methods, such as the randomly-shifted lattice rules in [63], enjoy a root-mean-squared error rate of O(n−1+δ) with δ ∈ (0, 1/2), where constant terms do not depend on dimension p.”
Multilevel Monte Carlo Path Simulation (2008, methodology): “The multilevel method is very easy to implement and can be combined, in principle, with other variance reduction methods such as strati(cid:12)ed sampling [7] and quasi Monte Carlo methods [16, 17, 19] to obtain even greater savings.”
Fast construction of good lattice rules (2007, background): “The graphical view on the permutations [81] accompanied the nice article on the complexity side of the story by Kuo and Sloan [64].”