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Generalized Scalar-on-Image Regression Models via Total Variation

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  • Xiao Wang
  • Hongtu Zhu

Abstract

The use of imaging markers to predict clinical outcomes can have a great impact in public health. The aim of this article is to develop a class of generalized scalar-on-image regression models via total variation (GSIRM-TV), in the sense of generalized linear models, for scalar response and imaging predictor with the presence of scalar covariates. A key novelty of GSIRM-TV is that it is assumed that the slope function (or image) of GSIRM-TV belongs to the space of bounded total variation to explicitly account for the piecewise smooth nature of most imaging data. We develop an efficient penalized total variation optimization to estimate the unknown slope function and other parameters. We also establish nonasymptotic error bounds on the excess risk. These bounds are explicitly specified in terms of sample size, image size, and image smoothness. Our simulations demonstrate a superior performance of GSIRM-TV against many existing approaches. We apply GSIRM-TV to the analysis of hippocampus data obtained from the Alzheimers Disease Neuroimaging Initiative (ADNI) dataset. Supplementary materials for this article are available online.

Suggested Citation

  • Xiao Wang & Hongtu Zhu, 2017. "Generalized Scalar-on-Image Regression Models via Total Variation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1156-1168, July.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:519:p:1156-1168
    DOI: 10.1080/01621459.2016.1194846
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    Cited by:

    1. Cui Guo & Jian Kang & Timothy D. Johnson, 2022. "A spatial Bayesian latent factor model for image‐on‐image regression," Biometrics, The International Biometric Society, vol. 78(1), pages 72-84, March.
    2. Baiguo An & Beibei Zhang, 2020. "Logistic regression with image covariates via the combination of L1 and Sobolev regularizations," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-18, June.
    3. Xu Gao & Weining Shen & Liwen Zhang & Jianhua Hu & Norbert J. Fortin & Ron D. Frostig & Hernando Ombao, 2021. "Regularized matrix data clustering and its application to image analysis," Biometrics, The International Biometric Society, vol. 77(3), pages 890-902, September.
    4. Wei Hu & Tianyu Pan & Dehan Kong & Weining Shen, 2021. "Nonparametric matrix response regression with application to brain imaging data analysis," Biometrics, The International Biometric Society, vol. 77(4), pages 1227-1240, December.
    5. Li, Yehua & Qiu, Yumou & Xu, Yuhang, 2022. "From multivariate to functional data analysis: Fundamentals, recent developments, and emerging areas," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    6. Yize Zhao & Ben Wu & Jian Kang, 2023. "Bayesian interaction selection model for multimodal neuroimaging data analysis," Biometrics, The International Biometric Society, vol. 79(2), pages 655-668, June.
    7. Weicheng Zhu & Sheng Xu & Catherine C. Liu & Yehua Li, 2023. "Minimax powerful functional analysis of covariance tests with application to longitudinal genome‐wide association studies," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 266-295, March.

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