Hierarchical Decompositions for the Computation of High-Dimensional Multivariate Normal Probabilities

Handle URI:
http://hdl.handle.net/10754/625457
Title:
Hierarchical Decompositions for the Computation of High-Dimensional Multivariate Normal Probabilities
Authors:
Genton, Marc G. ( 0000-0001-6467-2998 ) ; Keyes, David E. ( 0000-0002-4052-7224 ) ; Turkiyyah, George
Abstract:
We present a hierarchical decomposition scheme for computing the n-dimensional integral of multivariate normal probabilities that appear frequently in statistics. The scheme exploits the fact that the formally dense covariance matrix can be approximated by a matrix with a hierarchical low rank structure. It allows the reduction of the computational complexity per Monte Carlo sample from O(n2) to O(mn+knlog(n/m)), where k is the numerical rank of off-diagonal matrix blocks and m is the size of small diagonal blocks in the matrix that are not well-approximated by low rank factorizations and treated as dense submatrices. This hierarchical decomposition leads to substantial efficiencies in multivariate normal probability computations and allows integrations in thousands of dimensions to be practical on modern workstations.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Extreme Computing Research Center
Citation:
Genton MG, Keyes DE, Turkiyyah G (2017) Hierarchical Decompositions for the Computation of High-Dimensional Multivariate Normal Probabilities. Journal of Computational and Graphical Statistics: 0–0. Available: http://dx.doi.org/10.1080/10618600.2017.1375936.
Publisher:
Informa UK Limited
Journal:
Journal of Computational and Graphical Statistics
Issue Date:
7-Sep-2017
DOI:
10.1080/10618600.2017.1375936
Type:
Article
ISSN:
1061-8600; 1537-2715
Additional Links:
http://www.tandfonline.com/doi/full/10.1080/10618600.2017.1375936
Appears in Collections:
Articles; Extreme Computing Research Center; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorGenton, Marc G.en
dc.contributor.authorKeyes, David E.en
dc.contributor.authorTurkiyyah, Georgeen
dc.date.accessioned2017-09-14T06:03:52Z-
dc.date.available2017-09-14T06:03:52Z-
dc.date.issued2017-09-07en
dc.identifier.citationGenton MG, Keyes DE, Turkiyyah G (2017) Hierarchical Decompositions for the Computation of High-Dimensional Multivariate Normal Probabilities. Journal of Computational and Graphical Statistics: 0–0. Available: http://dx.doi.org/10.1080/10618600.2017.1375936.en
dc.identifier.issn1061-8600en
dc.identifier.issn1537-2715en
dc.identifier.doi10.1080/10618600.2017.1375936en
dc.identifier.urihttp://hdl.handle.net/10754/625457-
dc.description.abstractWe present a hierarchical decomposition scheme for computing the n-dimensional integral of multivariate normal probabilities that appear frequently in statistics. The scheme exploits the fact that the formally dense covariance matrix can be approximated by a matrix with a hierarchical low rank structure. It allows the reduction of the computational complexity per Monte Carlo sample from O(n2) to O(mn+knlog(n/m)), where k is the numerical rank of off-diagonal matrix blocks and m is the size of small diagonal blocks in the matrix that are not well-approximated by low rank factorizations and treated as dense submatrices. This hierarchical decomposition leads to substantial efficiencies in multivariate normal probability computations and allows integrations in thousands of dimensions to be practical on modern workstations.en
dc.publisherInforma UK Limiteden
dc.relation.urlhttp://www.tandfonline.com/doi/full/10.1080/10618600.2017.1375936en
dc.rightsThis is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Computational and Graphical Statistics on 07 Sep 2017, available online: http://wwww.tandfonline.com/10.1080/10618600.2017.1375936.en
dc.subjectHierarchical low-rank structureen
dc.subjectMax-stable processen
dc.subjectMultivariate cumulative distribution functionen
dc.subjectMultivariate skew-normal distributionen
dc.subjectSpatial statisticsen
dc.titleHierarchical Decompositions for the Computation of High-Dimensional Multivariate Normal Probabilitiesen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentExtreme Computing Research Centeren
dc.identifier.journalJournal of Computational and Graphical Statisticsen
dc.eprint.versionPost-printen
dc.contributor.institutionDepartment of Computer Science, American University of Beirut, Beirut, Lebanon.en
kaust.authorGenton, Marc G.en
kaust.authorKeyes, David E.en
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