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Fast tensorial JADE

Author

Listed:
  • Joni Virta
  • Niko Lietzén
  • Pauliina Ilmonen
  • Klaus Nordhausen

Abstract

We propose a novel method for tensorial‐independent component analysis. Our approach is based on TJADE and k‐JADE, two recently proposed generalizations of the classical JADE algorithm. Our novel method achieves the consistency and the limiting distribution of TJADE under mild assumptions and at the same time offers notable improvement in computational speed. Detailed mathematical proofs of the statistical properties of our method are given and, as a special case, a conjecture on the properties of k‐JADE is resolved. Simulations and timing comparisons demonstrate remarkable gain in speed. Moreover, the desired efficiency is obtained approximately for finite samples. The method is applied successfully to large‐scale video data, for which neither TJADE nor k‐JADE is feasible. Finally, an experimental procedure is proposed to select the values of a set of tuning parameters. Supplementary material including the R‐code for running the examples and the proofs of the theoretical results is available online.

Suggested Citation

  • Joni Virta & Niko Lietzén & Pauliina Ilmonen & Klaus Nordhausen, 2021. "Fast tensorial JADE," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 164-187, March.
    • Handle: RePEc:bla:scjsta:v:48:y:2021:i:1:p:164-187
    DOI: 10.1111/sjos.12445
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    References listed on IDEAS

    as
    1. Roś, Beata & Bijma, Fetsje & de Munck, Jan C. & de Gunst, Mathisca C.M., 2016. "Existence and uniqueness of the maximum likelihood estimator for models with a Kronecker product covariance structure," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 345-361.
    2. Miettinen, Jari & Nordhausen, Klaus & Taskinen, Sara, 2017. "Blind Source Separation Based on Joint Diagonalization in R: The Packages JADE and BSSasymp," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i02).
    3. Sirkku Pauliina Ilmonen & Davy Paindaveine, 2011. "Semiparametrically Efficient Inference Based on Signed Ranks in Symmetric Independent Component Models," Working Papers ECARES ECARES 2011-003, ULB -- Universite Libre de Bruxelles.
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