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Control functionals for quasi-Monte Carlo integration

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Title: Control functionals for quasi-Monte Carlo integration
Authors: Oates, CJ
Girolami, M
Item Type: Conference Paper
Abstract: Quasi-Monte Carlo (QMC) methods are being adopted in statistical applications due to the increasingly challenging nature of numerical integrals that are now routinely encountered. For integrands with d-dimensions and derivatives of order α, an optimal QMC rule converges at a best-possible rate O(N^-α/d). However, in applications the value of αcan be unknown and/or a rate-optimal QMC rule can be unavailable. Standard practice is to employ \alpha_L-optimal QMC where the lower bound \alpha_L ≤αis known, but in general this does not exploit the full power of QMC. One solution is to trade-off numerical integration with functional approximation. This strategy is explored herein and shown to be well-suited to modern statistical computation. A challenging application to robotic arm data demonstrates a substantial variance reduction in predictions for mechanical torques.
Issue Date: 2-May-2016
Date of Acceptance: 2-May-2016
URI: http://hdl.handle.net/10044/1/67110
Publisher: Proceedings of Machine Learning Research
Start Page: 56
End Page: 65
Journal / Book Title: Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR
Volume: 51
Copyright Statement: © 2016 The Author(s). This paper is published under a Creative Commons Attribution 4.0 International License, which is incorporated herein by reference and is further specified at http://creativecommons.org/licenses/by/4.0/legalcode (human readable summary at http://creativecommons.org/licenses/by/4.0).
Conference Name: 19th International Conference on Artificial Intelligence and Statistics
Keywords: stat.CO
Publication Status: Published
Start Date: 2016-05-09
Finish Date: 2016-05-11
Conference Place: Cadiz, Spain
Appears in Collections:Mathematics
Faculty of Natural Sciences