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Tucker Tensor Regression and Neuroimaging Analysis

Author

Listed:
  • Xiaoshan Li

    (Wells Fargo & Company)

  • Da Xu

    (University of California)

  • Hua Zhou

    (University of California)

  • Lexin Li

    (University of California)

Abstract

Neuroimaging data often take the form of high-dimensional arrays, also known as tensors. Addressing scientific questions arising from such data demands new regression models that take multidimensional arrays as covariates. Simply turning an image array into a vector would both cause extremely high dimensionality and destroy the inherent spatial structure of the array. In a recent work, Zhou et al. (J Am Stat Assoc, 108(502):540–552, 2013) proposed a family of generalized linear tensor regression models based upon the CP (CANDECOMP/PARAFAC) decomposition of regression coefficient array. Low-rank approximation brings the ultrahigh dimensionality to a manageable level and leads to efficient estimation. In this article, we propose a tensor regression model based on the more flexible Tucker decomposition. Compared to the CP model, Tucker regression model allows different number of factors along each mode. Such flexibility leads to several advantages that are particularly suited to neuroimaging analysis, including further reduction of the number of free parameters, accommodation of images with skewed dimensions, explicit modeling of interactions, and a principled way of image downsizing. We also compare the Tucker model with CP numerically on both simulated data and real magnetic resonance imaging data, and demonstrate its effectiveness in finite sample performance.

Suggested Citation

  • Xiaoshan Li & Da Xu & Hua Zhou & Lexin Li, 2018. "Tucker Tensor Regression and Neuroimaging Analysis," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 520-545, December.
  • Handle: RePEc:spr:stabio:v:10:y:2018:i:3:d:10.1007_s12561-018-9215-6
    DOI: 10.1007/s12561-018-9215-6
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    References listed on IDEAS

    as
    1. Yimei Li & Hongtu Zhu & Dinggang Shen & Weili Lin & John H. Gilmore & Joseph G. Ibrahim, 2011. "Multiscale adaptive regression models for neuroimaging data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 559-578, September.
    2. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    3. Philip T. Reiss & R. Todd Ogden, 2010. "Functional Generalized Linear Models with Images as Predictors," Biometrics, The International Biometric Society, vol. 66(1), pages 61-69, March.
    4. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    5. Hua Zhou & Lexin Li, 2014. "Regularized matrix regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(2), pages 463-483, March.
    6. Ledyard Tucker, 1966. "Some mathematical notes on three-mode factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 279-311, September.
    7. Hua Zhou & Lexin Li & Hongtu Zhu, 2013. "Tensor Regression with Applications in Neuroimaging Data Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 540-552, June.
    8. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    9. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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    Cited by:

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    2. Kim, Jonathan & Sandri, Brian J. & Rao, Raghavendra B. & Lock, Eric F., 2023. "Bayesian predictive modeling of multi-source multi-way data," Computational Statistics & Data Analysis, Elsevier, vol. 186(C).
    3. Chen, Yang & Luo, Ziyan & Kong, Lingchen, 2024. "Low-rank tensor regression for selection of grouped variables," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    4. Bo Wei & Limin Peng & Ying Guo & Amita Manatunga & Jennifer Stevens, 2023. "Tensor response quantile regression with neuroimaging data," Biometrics, The International Biometric Society, vol. 79(3), pages 1947-1958, September.
    5. Tianqi Sun & Weiyu Li & Lu Lin, 2024. "Matrix-variate generalized linear model with measurement error," Statistical Papers, Springer, vol. 65(6), pages 3935-3958, August.
    6. Ghannam, Mai & Nkurunziza, Sévérien, 2023. "Tensor Stein-rules in a generalized tensor regression model," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    7. Ke, Baofang & Zhao, Weihua & Wang, Lei, 2023. "Smoothed tensor quantile regression estimation for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).

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