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dc.contributor.authorAbdulah, Sameh
dc.contributor.authorLtaief, Hatem
dc.contributor.authorSun, Ying
dc.contributor.authorGenton, Marc G.
dc.contributor.authorKeyes, David E.
dc.date.accessioned2019-04-28T13:12:24Z
dc.date.available2019-04-28T13:12:24Z
dc.date.issued2018-04-24
dc.identifier.urihttp://hdl.handle.net/10754/632517
dc.description.abstractMaximum likelihood estimation is an important statistical technique for estimating missing data, for example in climate and environmental applications, which are usually large and feature data points that are irregularly spaced. In particular, the Gaussian log-likelihood function is the \emph{de facto} model, which operates on the resulting sizable dense covariance matrix. The advent of high performance systems with advanced computing power and memory capacity have enabled full simulations only for rather small dimensional climate problems, solved at the machine precision accuracy. The challenge for high dimensional problems lies in the computation requirements of the log-likelihood function, which necessitates ${\mathcal O}(n^2)$ storage and ${\mathcal O}(n^3)$ operations, where $n$ represents the number of given spatial locations. This prohibitive computational cost may be reduced by using approximation techniques that not only enable large-scale simulations otherwise intractable but also maintain the accuracy and the fidelity of the spatial statistics model. In this paper, we extend the Exascale GeoStatistics software framework (i.e., ExaGeoStat) to support the Tile Low-Rank (TLR) approximation technique, which exploits the data sparsity of the dense covariance matrix by compressing the off-diagonal tiles up to a user-defined accuracy threshold. The underlying linear algebra operations may then be carried out on this data compression format, which may ultimately reduce the arithmetic complexity of the maximum likelihood estimation and the corresponding memory footprint. Performance results of TLR-based computations on shared and distributed-memory systems attain up to 13X and 5X speedups, respectively, compared to full accuracy simulations using synthetic and real datasets (up to 2M), while ensuring adequate prediction accuracy.
dc.publisherarXiv
dc.relation.urlhttp://arxiv.org/abs/1804.09137v1
dc.relation.urlhttp://arxiv.org/pdf/1804.09137v1
dc.rightsArchived with thanks to arXiv
dc.titleTile Low-Rank Approximation of Large-Scale Maximum Likelihood Estimation on Manycore Architectures
dc.typePreprint
dc.contributor.departmentExtreme Computing Research Center
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentStatistics Program
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.eprint.versionPre-print
dc.identifier.arxivid1804.09137
kaust.personAbdulah, Sameh
kaust.personLtaief, Hatem
kaust.personSun, Ying
kaust.personGenton, Marc G.
kaust.personKeyes, David E.
refterms.dateFOA2019-04-29T06:53:30Z


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