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    ℋ-matrix techniques for approximating large covariance matrices and estimating its parameters

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    Type
    Article
    Authors
    Litvinenko, Alexander cc
    Genton, Marc G. cc
    Sun, Ying cc
    Keyes, David E. cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Extreme Computing Research Center
    Statistics Program
    Date
    2016-10-25
    Online Publication Date
    2016-10-25
    Print Publication Date
    2016-10
    Permanent link to this record
    http://hdl.handle.net/10754/623937
    
    Metadata
    Show full item record
    Abstract
    In this work the task is to use the available measurements to estimate unknown hyper-parameters (variance, smoothness parameter and covariance length) of the covariance function. We do it by maximizing the joint log-likelihood function. This is a non-convex and non-linear problem. To overcome cubic complexity in linear algebra, we approximate the discretised covariance function in the hierarchical (ℋ-) matrix format. The ℋ-matrix format has a log-linear computational cost and storage O(knlogn), where rank k is a small integer. On each iteration step of the optimization procedure the covariance matrix itself, its determinant and its Cholesky decomposition are recomputed within ℋ-matrix format. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Citation
    Litvinenko A, Genton M, Sun Y, Keyes D (2016) ℋ-matrix techniques for approximating large covariance matrices and estimating its parameters. PAMM 16: 731–732. Available: http://dx.doi.org/10.1002/pamm.201610354.
    Sponsors
    Alexander Litvinenko and his research work reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST), SRI UQ and ECRC Centers.
    Publisher
    Wiley
    Journal
    PAMM
    DOI
    10.1002/pamm.201610354
    Additional Links
    http://onlinelibrary.wiley.com/doi/10.1002/pamm.201610354/abstract
    ae974a485f413a2113503eed53cd6c53
    10.1002/pamm.201610354
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Statistics Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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