ℋ-matrix techniques for approximating large covariance matrices and estimating its parameters
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Extreme Computing Research Center
Statistics Program
Date
2016-10-25Online Publication Date
2016-10-25Print Publication Date
2016-10Permanent link to this record
http://hdl.handle.net/10754/623937
Metadata
Show full item recordAbstract
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
WileyJournal
PAMMAdditional Links
http://onlinelibrary.wiley.com/doi/10.1002/pamm.201610354/abstractae974a485f413a2113503eed53cd6c53
10.1002/pamm.201610354