ℋ-matrix techniques for approximating large covariance matrices and estimating its parameters
KAUST DepartmentExtreme Computing Research Center
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
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AbstractIn 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)
CitationLitvinenko 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.
SponsorsAlexander 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.