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Optimal Whitening and Decorrelation

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  • Agnan Kessy
  • Alex Lewin
  • Korbinian Strimmer

Abstract

Whitening, or sphering, is a common preprocessing step in statistical analysis to transform random variables to orthogonality. However, due to rotational freedom there are infinitely many possible whitening procedures. Consequently, there is a diverse range of sphering methods in use, for example, based on principal component analysis (PCA), Cholesky matrix decomposition, and zero-phase component analysis (ZCA), among others. Here, we provide an overview of the underlying theory and discuss five natural whitening procedures. Subsequently, we demonstrate that investigating the cross-covariance and the cross-correlation matrix between sphered and original variables allows to break the rotational invariance and to identify optimal whitening transformations. As a result we recommend two particular approaches: ZCA-cor whitening to produce sphered variables that are maximally similar to the original variables, and PCA-cor whitening to obtain sphered variables that maximally compress the original variables.

Suggested Citation

  • Agnan Kessy & Alex Lewin & Korbinian Strimmer, 2018. "Optimal Whitening and Decorrelation," The American Statistician, Taylor & Francis Journals, vol. 72(4), pages 309-314, October.
    • Handle: RePEc:taf:amstat:v:72:y:2018:i:4:p:309-314
    DOI: 10.1080/00031305.2016.1277159
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    Cited by:

    1. Damiano Brigo & Xiaoshan Huang & Andrea Pallavicini & Haitz Saez de Ocariz Borde, 2021. "Interpretability in deep learning for finance: a case study for the Heston model," Papers 2104.09476, arXiv.org.
    2. Priddle, Jacob W. & Drovandi, Christopher, 2023. "Transformations in semi-parametric Bayesian synthetic likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    3. Dirk Roeder & Georgi Dimitroff, 2020. "Volatility model calibration with neural networks a comparison between direct and indirect methods," Papers 2007.03494, arXiv.org.
    4. Loperfido, Nicola, 2024. "The skewness of mean–variance normal mixtures," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    5. Stan Lipovetsky, 2022. "Canonical Concordance Correlation Analysis," Mathematics, MDPI, vol. 11(1), pages 1-12, December.
    6. Jonathan Gillard & Emily O’Riordan & Anatoly Zhigljavsky, 2023. "Polynomial whitening for high-dimensional data," Computational Statistics, Springer, vol. 38(3), pages 1427-1461, September.
    7. Minati, Ludovico & Li, Chao & Bartels, Jim & Chakraborty, Parthojit & Li, Zixuan & Yoshimura, Natsue & Frasca, Mattia & Ito, Hiroyuki, 2023. "Accelerometer time series augmentation through externally driving a non-linear dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    8. Steen MAGNUSSEN, 2018. "An estimation strategy to protect against over-estimating precision in a LiDAR-based prediction of a stand mean," Journal of Forest Science, Czech Academy of Agricultural Sciences, vol. 64(12), pages 497-505.
    9. Nikita Moshkov & Michael Bornholdt & Santiago Benoit & Matthew Smith & Claire McQuin & Allen Goodman & Rebecca A. Senft & Yu Han & Mehrtash Babadi & Peter Horvath & Beth A. Cimini & Anne E. Carpenter , 2024. "Learning representations for image-based profiling of perturbations," Nature Communications, Nature, vol. 15(1), pages 1-17, December.
    10. Harold Doran, 2023. "A Collection of Numerical Recipes Useful for Building Scalable Psychometric Applications," Journal of Educational and Behavioral Statistics, , vol. 48(1), pages 37-69, February.
    11. Schosser, Josef, 2019. "Consistency between principal and agent with differing time horizons: Computing incentives under risk," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1113-1123.
    12. Wong, William & Tsuchiya, Naotsugu, 2020. "Evidence accumulation clustering using combinations of features," OSF Preprints epb6t, Center for Open Science.

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