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Generalized co-sparse factor regression

Author

Listed:
  • Mishra, Aditya
  • Dey, Dipak K.
  • Chen, Yong
  • Chen, Kun

Abstract

Multivariate regression techniques are commonly applied to explore the associations between large numbers of outcomes and predictors. In real-world applications, the outcomes are often of mixed types, including continuous measurements, binary indicators, and counts, and the observations may also be incomplete. Building upon the recent advances in mixed-outcome modeling and sparse matrix factorization, generalized co-sparse factor regression (GOFAR) is proposed, which utilizes the flexible vector generalized linear model framework and encodes the outcome dependency through a sparse singular value decomposition (SSVD) of the integrated natural parameter matrix. To avoid the estimation of the notoriously difficult joint SSVD, GOFAR proposes both sequential and parallel unit-rank estimation procedures. By combining the ideas of alternating convex search and majorization–minimization, an efficient algorithm is developed to solve the sparse unit-rank problem and implemented in the R package gofar. Extensive simulation studies and two real-world applications demonstrate the effectiveness of the proposed approach.

Suggested Citation

  • Mishra, Aditya & Dey, Dipak K. & Chen, Yong & Chen, Kun, 2021. "Generalized co-sparse factor regression," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:csdana:v:157:y:2021:i:c:s0167947320302188
    DOI: 10.1016/j.csda.2020.107127
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    References listed on IDEAS

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    1. Jochen Gorski & Frank Pfeuffer & Kathrin Klamroth, 2007. "Biconvex sets and optimization with biconvex functions: a survey and extensions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 373-407, December.
    2. Ian T. Jolliffe, 1982. "A Note on the Use of Principal Components in Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(3), pages 300-303, November.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    8. She, Yiyuan, 2012. "An iterative algorithm for fitting nonconvex penalized generalized linear models with grouped predictors," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2976-2990.
    9. 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.
    10. 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.
    11. 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.
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