Low-rank multi-parametric covariance identification
We propose a differential geometric approach for building families of low-rank covariance matrices, via interpolation on low-rank matrix manifolds. In contrast with standard parametric covariance classes, these families offer significant flexibility for problem-specific tailoring via the choice of “...
| Main Authors: | , , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Springer
2021
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| _version_ | 1797099169285931008 |
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| author | Musolas, A Massart, EM Hendrickx, JM Absil, P-A Marzouk, Y |
| author_facet | Musolas, A Massart, EM Hendrickx, JM Absil, P-A Marzouk, Y |
| author_sort | Musolas, A |
| collection | OXFORD |
| description | We propose a differential geometric approach for building families of low-rank covariance matrices, via interpolation on low-rank matrix manifolds. In contrast with standard parametric covariance classes, these families offer significant flexibility for problem-specific tailoring via the choice of “anchor” matrices for interpolation, for instance over a grid of relevant conditions describing the underlying stochastic process. The interpolation is computationally tractable in high dimensions, as it only involves manipulations of low-rank matrix factors. We also consider the problem of covariance identification, i.e., selecting the most representative member of the covariance family given a data set. In this setting, standard procedures such as maximum likelihood estimation are nontrivial because the covariance family is rank-deficient; we resolve this issue by casting the identification problem as distance minimization. We demonstrate the utility of these differential geometric families for interpolation and identification in a practical application: wind field covariance approximation for unmanned aerial vehicle navigation.
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| first_indexed | 2024-03-07T05:19:51Z |
| format | Journal article |
| id | oxford-uuid:de83f03d-0fb1-468f-9790-8ea39af33c93 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:19:51Z |
| publishDate | 2021 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:de83f03d-0fb1-468f-9790-8ea39af33c932022-03-27T09:32:43ZLow-rank multi-parametric covariance identificationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:de83f03d-0fb1-468f-9790-8ea39af33c93EnglishSymplectic ElementsSpringer2021Musolas, AMassart, EMHendrickx, JMAbsil, P-AMarzouk, YWe propose a differential geometric approach for building families of low-rank covariance matrices, via interpolation on low-rank matrix manifolds. In contrast with standard parametric covariance classes, these families offer significant flexibility for problem-specific tailoring via the choice of “anchor” matrices for interpolation, for instance over a grid of relevant conditions describing the underlying stochastic process. The interpolation is computationally tractable in high dimensions, as it only involves manipulations of low-rank matrix factors. We also consider the problem of covariance identification, i.e., selecting the most representative member of the covariance family given a data set. In this setting, standard procedures such as maximum likelihood estimation are nontrivial because the covariance family is rank-deficient; we resolve this issue by casting the identification problem as distance minimization. We demonstrate the utility of these differential geometric families for interpolation and identification in a practical application: wind field covariance approximation for unmanned aerial vehicle navigation. |
| spellingShingle | Musolas, A Massart, EM Hendrickx, JM Absil, P-A Marzouk, Y Low-rank multi-parametric covariance identification |
| title | Low-rank multi-parametric covariance identification |
| title_full | Low-rank multi-parametric covariance identification |
| title_fullStr | Low-rank multi-parametric covariance identification |
| title_full_unstemmed | Low-rank multi-parametric covariance identification |
| title_short | Low-rank multi-parametric covariance identification |
| title_sort | low rank multi parametric covariance identification |
| work_keys_str_mv | AT musolasa lowrankmultiparametriccovarianceidentification AT massartem lowrankmultiparametriccovarianceidentification AT hendrickxjm lowrankmultiparametriccovarianceidentification AT absilpa lowrankmultiparametriccovarianceidentification AT marzouky lowrankmultiparametriccovarianceidentification |