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Leveraging mixed and incomplete outcomes via reduced-rank modeling

Author

Listed:
  • Luo, Chongliang
  • Liang, Jian
  • Li, Gen
  • Wang, Fei
  • Zhang, Changshui
  • Dey, Dipak K.
  • Chen, Kun

Abstract

Multivariate outcomes with multivariate features of possibly high dimension are routinely produced in various fields. In many real-world problems, the collected outcomes are of mixed types, including continuous measurements, binary indicators and counts, and a substantial proportion of values may also be missing. Regardless of their types, these mixed outcomes are often interrelated, representing diverse reflections or views of the same underlying data generation mechanism. As such, an integrative multivariate model can be beneficial. We develop a mixed-outcome reduced-rank regression, which effectively enables information sharing among different prediction tasks. Our approach integrates mixed and partially observed outcomes belonging to the exponential dispersion family, by assuming that all the outcomes are associated through a shared low-dimensional subspace spanned by the features. A general singular value regularized criterion is proposed, and we establish a non-asymptotic performance bound for the proposed estimators in the context of supervised learning with mixed outcomes from an exponential family and under a general sampling scheme of missing data. An iterative singular value thresholding algorithm is developed for optimization with convergence guarantee. The effectiveness of our approach is demonstrated by simulation studies and an application on predicting health-related outcomes in longitudinal studies of aging.

Suggested Citation

  • Luo, Chongliang & Liang, Jian & Li, Gen & Wang, Fei & Zhang, Changshui & Dey, Dipak K. & Chen, Kun, 2018. "Leveraging mixed and incomplete outcomes via reduced-rank modeling," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 378-394.
    • Handle: RePEc:eee:jmvana:v:167:y:2018:i:c:p:378-394
    DOI: 10.1016/j.jmva.2018.04.011
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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Y. She & K. Chen, 2017. "Robust reduced-rank regression," Biometrika, Biometrika Trust, vol. 104(3), pages 633-647.
    3. R. Dennis Cook & Liliana Forzani & Xin Zhang, 2015. "Envelopes and reduced-rank regression," Biometrika, Biometrika Trust, vol. 102(2), pages 439-456.
    4. Li, Bing & Wen, Songqiao & Zhu, Lixing, 2008. "On a Projective Resampling Method for Dimension Reduction With Multivariate Responses," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1177-1186.
    5. Lexin Li & Xin Zhang, 2017. "Parsimonious Tensor Response Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1131-1146, July.
    6. Ming Yuan & Ali Ekici & Zhaosong Lu & Renato Monteiro, 2007. "Dimension reduction and coefficient estimation in multivariate linear regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 329-346, June.
    7. A. Mukherjee & K. Chen & N. Wang & J. Zhu, 2015. "On the degrees of freedom of reduced-rank estimators in multivariate regression," Biometrika, Biometrika Trust, vol. 102(2), pages 457-477.
    8. Fan, Yanan & de Micheaux, Pierre Lafaye & Penev, Spiridon & Salopek, Donna, 2017. "Multivariate nonparametric test of independence," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 189-210.
    9. 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.
    10. Mary Dupuis Sammel & Louise M. Ryan & Julie M. Legler, 1997. "Latent Variable Models for Mixed Discrete and Continuous Outcomes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(3), pages 667-678.
    11. Yingying Fan & Jinchi Lv, 2013. "Asymptotic Equivalence of Regularization Methods in Thresholded Parameter Space," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1044-1061, September.
    12. Kun Chen & Kung‐Sik Chan & Nils Chr. Stenseth, 2012. "Reduced rank stochastic regression with a sparse singular value decomposition," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(2), pages 203-221, March.
    13. Kun Chen & Hongbo Dong & Kung-Sik Chan, 2013. "Reduced rank regression via adaptive nuclear norm penalization," Biometrika, Biometrika Trust, vol. 100(4), pages 901-920.
    14. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    15. D. B. Dunson, 2000. "Bayesian latent variable models for clustered mixed outcomes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 355-366.
    16. Lisha Chen & Jianhua Z. Huang, 2012. "Sparse Reduced-Rank Regression for Simultaneous Dimension Reduction and Variable Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1533-1545, December.
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    3. Mishra, Aditya & Dey, Dipak K. & Chen, Yong & Chen, Kun, 2021. "Generalized co-sparse factor regression," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).

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