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Covariate-Adjusted Tensor Classification in High Dimensions

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  • Yuqing Pan
  • Qing Mai
  • Xin Zhang

Abstract

In contemporary scientific research, it is often of great interest to predict a categorical response based on a high-dimensional tensor (i.e., multi-dimensional array) and additional covariates. Motivated by applications in science and engineering, we propose a comprehensive and interpretable discriminant analysis model, called the CATCH model (short for covariate-adjusted tensor classification in high-dimensions). The CATCH model efficiently integrates the covariates and the tensor to predict the categorical outcome. It also jointly explains the complicated relationships among the covariates, the tensor predictor, and the categorical response. The tensor structure is used to achieve easy interpretation and accurate prediction. To tackle the new computational and statistical challenges arising from the intimidating tensor dimensions, we propose a penalized approach to select a subset of the tensor predictor entries that affect classification after adjustment for the covariates. An efficient algorithm is developed to take advantage of the tensor structure in the penalized estimation. Theoretical results confirm that the proposed method achieves variable selection and prediction consistency, even when the tensor dimension is much larger than the sample size. The superior performance of our method over existing methods is demonstrated in extensive simulated and real data examples. Supplementary materials for this article are available online.

Suggested Citation

  • Yuqing Pan & Qing Mai & Xin Zhang, 2019. "Covariate-Adjusted Tensor Classification in High Dimensions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1305-1319, July.
  • Handle: RePEc:taf:jnlasa:v:114:y:2019:i:527:p:1305-1319
    DOI: 10.1080/01621459.2018.1497500
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    Cited by:

    1. Pan, Yuqing & Mai, Qing, 2020. "Efficient computation for differential network analysis with applications to quadratic discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    2. Inkoo Lee & Debajyoti Sinha & Qing Mai & Xin Zhang & Dipankar Bandyopadhyay, 2023. "Bayesian regression analysis of skewed tensor responses," Biometrics, The International Biometric Society, vol. 79(3), pages 1814-1825, September.
    3. Zengchao Xu & Shan Luo & Zehua Chen, 2023. "A Portmanteau Local Feature Discrimination Approach to the Classification with High-dimensional Matrix-variate Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 441-467, February.
    4. Lu, Wenqi & Zhu, Zhongyi & Li, Rui & Lian, Heng, 2024. "Statistical performance of quantile tensor regression with convex regularization," Journal of Multivariate Analysis, Elsevier, vol. 200(C).
    5. Kai Deng & Xin Zhang, 2022. "Tensor envelope mixture model for simultaneous clustering and multiway dimension reduction," Biometrics, The International Biometric Society, vol. 78(3), pages 1067-1079, September.

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