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The use of the r* heuristic in covariance completion problems

Grussler, Christian LU ; Zare, Armin ; Jovanović, Mihailo and Rantzer, Anders LU orcid (2016) 55th IEEE Conference on Decision and Control 2016
Abstract
We consider a class of structured covariance completion problems which aim to complete partially known sample statistics in a way that is consistent with the underlying linear dynamics. The statistics of stochastic inputs are unknown and sought to explain the given correlations. Such inverse problems admit many solutions for the forcing correlations, but can be interpreted as an optimal low-rank approximation problem for identifying forcing models of low complexity. On the other hand, the quality of completion can be improved by utilizing information regarding the magnitude of unknown entries. We generalize theoretical results regarding the r* norm approximation and demonstrate the performance of this heuristic in completing partially... (More)
We consider a class of structured covariance completion problems which aim to complete partially known sample statistics in a way that is consistent with the underlying linear dynamics. The statistics of stochastic inputs are unknown and sought to explain the given correlations. Such inverse problems admit many solutions for the forcing correlations, but can be interpreted as an optimal low-rank approximation problem for identifying forcing models of low complexity. On the other hand, the quality of completion can be improved by utilizing information regarding the magnitude of unknown entries. We generalize theoretical results regarding the r* norm approximation and demonstrate the performance of this heuristic in completing partially available statistics using stochastically-driven linear models. (Less)
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author
; ; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
2016 IEEE 55th Conference on Decision and Control (CDC)
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
55th IEEE Conference on Decision and Control 2016
conference location
Las Vegas, NV, United States
conference dates
2016-09-12 - 2016-09-14
external identifiers
  • scopus:85010735036
ISBN
978-1-5090-1837-6
978-1-5090-1838-3
DOI
10.1109/CDC.2016.7798554
language
English
LU publication?
yes
id
a61669c7-29b9-41ee-82da-9c825b08f8d8
date added to LUP
2017-02-23 17:34:09
date last changed
2025-01-07 08:17:58
@inproceedings{a61669c7-29b9-41ee-82da-9c825b08f8d8,
  abstract     = {{We consider a class of structured covariance completion problems which aim to complete partially known sample statistics in a way that is consistent with the underlying linear dynamics. The statistics of stochastic inputs are unknown and sought to explain the given correlations. Such inverse problems admit many solutions for the forcing correlations, but can be interpreted as an optimal low-rank approximation problem for identifying forcing models of low complexity. On the other hand, the quality of completion can be improved by utilizing information regarding the magnitude of unknown entries. We generalize theoretical results regarding the r* norm approximation and demonstrate the performance of this heuristic in completing partially available statistics using stochastically-driven linear models.}},
  author       = {{Grussler, Christian and Zare, Armin and Jovanović, Mihailo and Rantzer, Anders}},
  booktitle    = {{2016 IEEE 55th Conference on Decision and Control (CDC)}},
  isbn         = {{978-1-5090-1837-6}},
  language     = {{eng}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{The use of the r* heuristic in covariance completion problems}},
  url          = {{https://lup.lub.lu.se/search/files/21812420/2016cdcGrussler_.pdf}},
  doi          = {{10.1109/CDC.2016.7798554}},
  year         = {{2016}},
}