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Supervised classifiers for high-dimensional higher-order data with locally doubly exchangeable covariance structure
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2017 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 46, no 23, p. 11612-11634Article in journal (Refereed) Published
Abstract [en]

We explore the performance accuracy of the linear and quadratic classifiers for high-dimensional higher-order data, assuming that the class conditional distributions are multivariate normal with locally doubly exchangeable covariance structure. We derive a two-stage procedure for estimating the covariance matrix: at the first stage, the Lasso-based structure learning is applied to sparsifying the block components within the covariance matrix. At the second stage, the maximum-likelihood estimators of all block-wise parameters are derived assuming the doubly exchangeable within block covariance structure and a Kronecker product structured mean vector. We also study the effect of the block size on the classification performance in the high-dimensional setting and derive a class of asymptotically equivalent block structure approximations, in a sense that the choice of the block size is asymptotically negligible.

Place, publisher, year, edition, pages
Taylor & Francis, 2017. Vol. 46, no 23, p. 11612-11634
Keywords [en]
Class of asymptotically equivalent structure approximations, classification rule, graphical Lasso, high-dimensional higher-order data, locally doubly exchangeable covariance structure
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-219527DOI: 10.1080/03610926.2016.1275695ISI: 000415942200014Scopus ID: 2-s2.0-85029411318OAI: oai:DiVA.org:kth-219527DiVA, id: diva2:1163447
Funder
Swedish Research Council, 421-2008-1966The Royal Swedish Academy of Sciences
Note

QC 20171207

Available from: 2017-12-07 Created: 2017-12-07 Last updated: 2017-12-07Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
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