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Uncertainty quantification via codimension one domain partitioning and a new concentration inequality

Sullivan, Timothy J. and McKerns, Mike and Topcu, Ufuk and Owhadi, Houman (2010) Uncertainty quantification via codimension one domain partitioning and a new concentration inequality. Procedia - Social and Behavioral Sciences, 2 (6). pp. 7751-7752. ISSN 1877-0428. https://resolver.caltech.edu/CaltechAUTHORS:20190109-104739732

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Abstract

In [LOO08], it was proposed that a concentration-of-measure inequality known as Mc-Diarmid’s inequality [McD89] be used to provide upper bounds on the failure probability of a system of interest, the response of which depends on a collection of independent random inputs. McDiarmid’s inequality has the advantage of providing an upper bound in terms of only the mean response of the system, the failure threshold, and measures of system spread known as the McDiarmid subdiameters. A disadvantage of McDiarmid’s inequality is that it that takes a global view of the response function: even if the response function exhibits large plateaus of success with only small, localized regions of failure, McDiarmid’s inequality is unable to use this to any advantage. We propose a partitioning algorithm that uses McDiarmid diameters to generate “good” sequences of partitions, on which McDiarmid’s inequality can be applied to each partition element, yielding arbitrarily tight upper bounds. We also investigate some new concentration-of-measure inequalities that arise if mean performance is known only through sampling.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.sbspro.2010.05.211DOIArticle
ORCID:
AuthorORCID
Owhadi, Houman0000-0002-5677-1600
Additional Information:© 2010 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. Available online 29 June 2010.
Issue or Number:6
Record Number:CaltechAUTHORS:20190109-104739732
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190109-104739732
Official Citation:Timothy J. Sullivan, Mike McKerns, Ufuk Topcu, Houman Owhadi, Uncertainty quantification via codimension one domain partitioning and a new concentration inequality, Procedia - Social and Behavioral Sciences, Volume 2, Issue 6, 2010, Pages 7751-7752, ISSN 1877-0428, https://doi.org/10.1016/j.sbspro.2010.05.211. (http://www.sciencedirect.com/science/article/pii/S1877042810013522)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92163
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Jan 2019 18:54
Last Modified:03 Oct 2019 20:41

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