Control functionals for quasi-Monte Carlo integration
File(s)
Published version
Author(s)
Oates, Chris J
Girolami, Mark
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.
Date Issued
2016-05-02
Date Acceptance
2016-05-02
Citation
Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR, 2016, 51, pp.56-65
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).
specified at http://creativecommons.org/licenses/by/4.0/legalcode (human readable summary at http://creativecommons.org/licenses/by/4.0).
Source
19th International Conference on Artificial Intelligence and Statistics
Subjects
stat.CO
stat.CO
Publication Status
Published
Start Date
2016-05-09
Finish Date
2016-05-11
Coverage Spatial
Cadiz, Spain