Handle URI:
http://hdl.handle.net/10754/598738
Title:
Low cost high performance uncertainty quantification
Authors:
Bekas, C.; Curioni, A.; Fedulova, I.
Abstract:
Uncertainty quantification in risk analysis has become a key application. In this context, computing the diagonal of inverse covariance matrices is of paramount importance. Standard techniques, that employ matrix factorizations, incur a cubic cost which quickly becomes intractable with the current explosion of data sizes. In this work we reduce this complexity to quadratic with the synergy of two algorithms that gracefully complement each other and lead to a radically different approach. First, we turned to stochastic estimation of the diagonal. This allowed us to cast the problem as a linear system with a relatively small number of multiple right hand sides. Second, for this linear system we developed a novel, mixed precision, iterative refinement scheme, which uses iterative solvers instead of matrix factorizations. We demonstrate that the new framework not only achieves the much needed quadratic cost but in addition offers excellent opportunities for scaling at massively parallel environments. We based our implementation on BLAS 3 kernels that ensure very high processor performance. We achieved a peak performance of 730 TFlops on 72 BG/P racks, with a sustained performance 73% of theoretical peak. We stress that the techniques presented in this work are quite general and applicable to several other important applications. Copyright © 2009 ACM.
Citation:
Bekas C, Curioni A, Fedulova I (2009) Low cost high performance uncertainty quantification. Proceedings of the 2nd Workshop on High Performance Computational Finance - WHPCF ’09. Available: http://dx.doi.org/10.1145/1645413.1645421.
Publisher:
Association for Computing Machinery (ACM)
Journal:
Proceedings of the 2nd Workshop on High Performance Computational Finance - WHPCF '09
Issue Date:
2009
DOI:
10.1145/1645413.1645421
Type:
Conference Paper
Sponsors:
The authors gratefully acknowledge Prof. Thomas Lippertand the Julich Supercomputing Center for kindly grantingaccess to their 72 rack BG/P cluster. We also would likethe thank for the support of WatsonShaheen - an 8 rackBlue Gene/P Supercomputer at IBM's T.J. Watson ResearchCenter that is jointly owned and managed by the KingAbdullah University of Science and Technology (KAUST)and IBM.
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorBekas, C.en
dc.contributor.authorCurioni, A.en
dc.contributor.authorFedulova, I.en
dc.date.accessioned2016-02-25T13:40:13Zen
dc.date.available2016-02-25T13:40:13Zen
dc.date.issued2009en
dc.identifier.citationBekas C, Curioni A, Fedulova I (2009) Low cost high performance uncertainty quantification. Proceedings of the 2nd Workshop on High Performance Computational Finance - WHPCF ’09. Available: http://dx.doi.org/10.1145/1645413.1645421.en
dc.identifier.doi10.1145/1645413.1645421en
dc.identifier.urihttp://hdl.handle.net/10754/598738en
dc.description.abstractUncertainty quantification in risk analysis has become a key application. In this context, computing the diagonal of inverse covariance matrices is of paramount importance. Standard techniques, that employ matrix factorizations, incur a cubic cost which quickly becomes intractable with the current explosion of data sizes. In this work we reduce this complexity to quadratic with the synergy of two algorithms that gracefully complement each other and lead to a radically different approach. First, we turned to stochastic estimation of the diagonal. This allowed us to cast the problem as a linear system with a relatively small number of multiple right hand sides. Second, for this linear system we developed a novel, mixed precision, iterative refinement scheme, which uses iterative solvers instead of matrix factorizations. We demonstrate that the new framework not only achieves the much needed quadratic cost but in addition offers excellent opportunities for scaling at massively parallel environments. We based our implementation on BLAS 3 kernels that ensure very high processor performance. We achieved a peak performance of 730 TFlops on 72 BG/P racks, with a sustained performance 73% of theoretical peak. We stress that the techniques presented in this work are quite general and applicable to several other important applications. Copyright © 2009 ACM.en
dc.description.sponsorshipThe authors gratefully acknowledge Prof. Thomas Lippertand the Julich Supercomputing Center for kindly grantingaccess to their 72 rack BG/P cluster. We also would likethe thank for the support of WatsonShaheen - an 8 rackBlue Gene/P Supercomputer at IBM's T.J. Watson ResearchCenter that is jointly owned and managed by the KingAbdullah University of Science and Technology (KAUST)and IBM.en
dc.publisherAssociation for Computing Machinery (ACM)en
dc.subjectInverse covariance matricesen
dc.subjectIterative refinementen
dc.subjectIterative solversen
dc.subjectMassive parallelismen
dc.subjectQuadratic costen
dc.subjectStochastic estimationen
dc.titleLow cost high performance uncertainty quantificationen
dc.typeConference Paperen
dc.identifier.journalProceedings of the 2nd Workshop on High Performance Computational Finance - WHPCF '09en
dc.contributor.institutionIBM Zurich Research Laboratory, Ruschlikon, Switzerlanden
dc.contributor.institutionInternational Business Machines, Armonk, United Statesen
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