Optimal uncertainty quantification for legacy data observations of Lipschitz functions

Details Optimal uncertainty quantification for legacy data observations of Lipschitz functions Optimal uncertainty quantification for legacy data observations of Lipschitz functions

2012-02-09

arxiv.org/abs/1202.1928v1

Mathematics

Probability

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Optimal uncertainty quantification for legacy data observations of Lipschitz functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Optimal uncertainty quantification for legacy data observations of Lipschitz functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Optimal uncertainty quantification for legacy data observations of Lipschitz functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-156614