• Login
    View Item 
    •   Home
    • Research
    • Preprints
    • View Item
    •   Home
    • Research
    • Preprints
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of KAUSTCommunitiesIssue DateSubmit DateThis CollectionIssue DateSubmit Date

    My Account

    Login

    Quick Links

    Open Access PolicyORCID LibguidePlumX LibguideSubmit an Item

    Statistics

    Display statistics

    Tile Low-Rank Approximation of Large-Scale Maximum Likelihood Estimation on Manycore Architectures

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    Name:
    1804.09137v1.pdf
    Size:
    2.731Mb
    Format:
    PDF
    Description:
    Preprint
    Download
    Type
    Preprint
    Authors
    Abdulah, Sameh
    Ltaief, Hatem cc
    Sun, Ying cc
    Genton, Marc G. cc
    Keyes, David E. cc
    KAUST Department
    Extreme Computing Research Center
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    Applied Mathematics and Computational Science Program
    Date
    2018-04-24
    Permanent link to this record
    http://hdl.handle.net/10754/632517
    
    Metadata
    Show full item record
    Abstract
    Maximum 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.
    Publisher
    arXiv
    arXiv
    1804.09137
    Additional Links
    http://arxiv.org/abs/1804.09137v1
    http://arxiv.org/pdf/1804.09137v1
    Collections
    Preprints; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Statistics Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

    entitlement

     
    DSpace software copyright © 2002-2021  DuraSpace
    Quick Guide | Contact Us | Send Feedback
    Open Repository is a service hosted by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items. For anonymous users the allowed maximum amount is 50 search results.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.