Likelihood Approximation With Parallel Hierarchical Matrices For Large Spatial Datasets

Handle URI:
http://hdl.handle.net/10754/626107
Title:
Likelihood Approximation With Parallel Hierarchical Matrices For Large Spatial Datasets
Authors:
Litvinenko, Alexander ( 0000-0001-5427-3598 ) ; Sun, Ying ( 0000-0001-6703-4270 ) ; Genton, Marc G. ( 0000-0001-6467-2998 ) ; Keyes, David E. ( 0000-0002-4052-7224 )
Abstract:
The main goal of this article is to introduce the parallel hierarchical matrix library HLIBpro to the statistical community. We describe the HLIBCov package, which is an extension of the HLIBpro library for approximating large covariance matrices and maximizing likelihood functions. We show that an approximate Cholesky factorization of a dense matrix of size $2M\times 2M$ can be computed on a modern multi-core desktop in few minutes. Further, HLIBCov is used for estimating the unknown parameters such as the covariance length, variance and smoothness parameter of a Matérn covariance function by maximizing the joint Gaussian log-likelihood function. The computational bottleneck here is expensive linear algebra arithmetics due to large and dense covariance matrices. Therefore covariance matrices are approximated in the hierarchical ($\H$-) matrix format with computational cost $\mathcal{O}(k^2n \log^2 n/p)$ and storage $\mathcal{O}(kn \log n)$, where the rank $k$ is a small integer (typically $k<25$), $p$ the number of cores and $n$ the number of locations on a fairly general mesh. We demonstrate a synthetic example, where the true values of known parameters are known. For reproducibility we provide the C++ code, the documentation, and the synthetic data.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Conference/Event name:
Workshop: Modern Statistics for Complex Data Structures
Issue Date:
1-Nov-2017
Type:
Poster
Sponsors:
KAUST
Is Version Of:
http://hdl.handle.net/10754/623348
Additional Links:
https://stat.kaust.edu.sa/calender/Pages/Page-2017-04-26_11-07-06-AM.aspx
Appears in Collections:
Posters

Full metadata record

DC FieldValue Language
dc.contributor.authorLitvinenko, Alexanderen
dc.contributor.authorSun, Yingen
dc.contributor.authorGenton, Marc G.en
dc.contributor.authorKeyes, David E.en
dc.date.accessioned2017-11-05T07:36:42Z-
dc.date.available2017-11-05T07:36:42Z-
dc.date.issued2017-11-01-
dc.identifier.urihttp://hdl.handle.net/10754/626107-
dc.description.abstractThe main goal of this article is to introduce the parallel hierarchical matrix library HLIBpro to the statistical community. We describe the HLIBCov package, which is an extension of the HLIBpro library for approximating large covariance matrices and maximizing likelihood functions. We show that an approximate Cholesky factorization of a dense matrix of size $2M\times 2M$ can be computed on a modern multi-core desktop in few minutes. Further, HLIBCov is used for estimating the unknown parameters such as the covariance length, variance and smoothness parameter of a Matérn covariance function by maximizing the joint Gaussian log-likelihood function. The computational bottleneck here is expensive linear algebra arithmetics due to large and dense covariance matrices. Therefore covariance matrices are approximated in the hierarchical ($\H$-) matrix format with computational cost $\mathcal{O}(k^2n \log^2 n/p)$ and storage $\mathcal{O}(kn \log n)$, where the rank $k$ is a small integer (typically $k<25$), $p$ the number of cores and $n$ the number of locations on a fairly general mesh. We demonstrate a synthetic example, where the true values of known parameters are known. For reproducibility we provide the C++ code, the documentation, and the synthetic data.en
dc.description.sponsorshipKAUSTen
dc.relation.isversionofhttp://hdl.handle.net/10754/623348en
dc.relation.urlhttps://stat.kaust.edu.sa/calender/Pages/Page-2017-04-26_11-07-06-AM.aspxen
dc.subjectparallelen
dc.subjecthierarchical matricesen
dc.subjectUncertaintyen
dc.subjectParameter identificationen
dc.subjectloglikelihooden
dc.subjectMatern covarianceen
dc.titleLikelihood Approximation With Parallel Hierarchical Matrices For Large Spatial Datasetsen
dc.typePosteren
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.conference.dateNov. 12-15, 2017en
dc.conference.nameWorkshop: Modern Statistics for Complex Data Structuresen
dc.conference.locationKAUSTen
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