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l1 regularized multiplicative iterative path algorithm for non-negative generalized linear models

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  • Mandal, B.N.
  • Ma, Jun

Abstract

In regression modeling, often a restriction that regression coefficients are non-negative is faced. The problem of model selection in non-negative generalized linear models (NNGLM) is considered using lasso, where regression coefficients in the linear predictor are subject to non-negative constraints. Thus, non-negatively constrained regression coefficient estimation is sought by maximizing the penalized likelihood (such as the l1-norm penalty). An efficient regularization path algorithm is proposed for generalized linear models with non-negative regression coefficients. The algorithm uses multiplicative updates which are fast and simultaneous. Asymptotic results are also developed for the constrained penalized likelihood estimates. Performance of the proposed algorithm is shown in terms of computational time, accuracy of solutions and accuracy of asymptotic standard deviations.

Suggested Citation

  • Mandal, B.N. & Ma, Jun, 2016. "l1 regularized multiplicative iterative path algorithm for non-negative generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 289-299.
    • Handle: RePEc:eee:csdana:v:101:y:2016:i:c:p:289-299
    DOI: 10.1016/j.csda.2016.03.009
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    References listed on IDEAS

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    1. Ma, Jun & Heritier, Stephane & Lô, Serigne N., 2014. "On the maximum penalized likelihood approach for proportional hazard models with right censored survival data," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 142-156.
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    4. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    5. 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.
    6. 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.
    7. Honore, Bo E. & Powell, James L., 1994. "Pairwise difference estimators of censored and truncated regression models," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 241-278.
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    Cited by:

    1. Xiaofei Wu & Rongmei Liang & Hu Yang, 2022. "Penalized and constrained LAD estimation in fixed and high dimension," Statistical Papers, Springer, vol. 63(1), pages 53-95, February.
    2. Shanshan Qin & Hao Ding & Yuehua Wu & Feng Liu, 2021. "High-dimensional sign-constrained feature selection and grouping," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(4), pages 787-819, August.

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