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Published November 2013 | Published + Submitted
Journal Article Open

Optimal Uncertainty Quantification for Legacy Data Observations of Lipschitz Functions


We consider the problem of providing optimal uncertainty quantification (UQ) – and hence rigorous certification – for partially-observed functions. We present a UQ framework within which the observations may be small or large in number, and need not carry information about the probability distribution of the system in operation. The UQ objectives are posed as optimization problems, the solutions of which are optimal bounds on the quantities of interest; we consider two typical settings, namely parameter sensitivities (McDiarmid diameters) and output deviation (or failure) probabilities. The solutions of these optimization problems depend non-trivially (even non-monotonically and discontinuously) upon the specified legacy data. Furthermore, the extreme values are often determined by only a few members of the data set; in our principal physically-motivated example, the bounds are determined by just 2 out of 32 data points, and the remainder carry no information and could be neglected without changing the final answer. We propose an analogue of the simplex algorithm from linear programming that uses these observations to offer efficient and rigorous UQ for high-dimensional systems with high-cardinality legacy data. These findings suggest natural methods for selecting optimal (maximally informative) next experiments.

Additional Information

© 2013 EDP Sciences, SMAI. Article published by EDP Sciences. Received February 9, 2012. Published online by Cambridge University Press: 30 August 2013. Portions of this work were supported by the US Department of Energy NNSA under award DEFC52-08NA28613 through the California Institute of Technology's ASC/PSAAP Center for the Predictive Modeling and Simulation of High Energy Density Dynamic Response of Materials. We thank the California Institute of Technology PSAAP Center's Experimental Science Group – in particular, M. Adams, J.M. Mihaly and A. Rosakis – for the data set in Table 1. Finally, we thank three anonymous referees for their helpful comments.

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Submitted - 1202.1928.pdf

Published - Sullivan_2013p1657.pdf


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August 22, 2023
August 22, 2023