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Primal path algorithm for compositional data analysis

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  • Jeon, Jong-June
  • Kim, Yongdai
  • Won, Sungho
  • Choi, Hosik

Abstract

We consider the LASSO estimator for compositional data in which covariates are nonnegative, and their sum is always one. Due to the linear constraint of the regression coefficients caused by the sum to one condition, standard algorithms for LASSO cannot be applied directly to compositional data. Hence, a specific regularized regression model with linear constraints is commonly used. However, linear constraints incur additional computational time, which becomes severe in high-dimensional cases. Additionally, the exact computation for the regression is not investigated under existing methods. In this paper, we first propose an exact solution path algorithm for a l1 regularized regression with high-dimensional compositional data and extend to a classification model. We also compare its computational speed with that of previously developed algorithms and then apply the proposed algorithm to analyzing income inequality data in economics and human gut microbiome data in biology. By analyzing simulated and real data sets, we illustrate that our specialized algorithm is significantly more efficient than the generalized LASSO algorithm for compositional data.

Suggested Citation

  • Jeon, Jong-June & Kim, Yongdai & Won, Sungho & Choi, Hosik, 2020. "Primal path algorithm for compositional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).
    • Handle: RePEc:eee:csdana:v:148:y:2020:i:c:s0167947320300499
    DOI: 10.1016/j.csda.2020.106958
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    References listed on IDEAS

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    1. Wei Lin & Pixu Shi & Rui Feng & Hongzhe Li, 2014. "Variable selection in regression with compositional covariates," Biometrika, Biometrika Trust, vol. 101(4), pages 785-797.
    2. Nicolai Meinshausen & Peter Bühlmann, 2010. "Stability selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 417-473, September.
    3. P. Tseng & S. Yun, 2009. "Block-Coordinate Gradient Descent Method for Linearly Constrained Nonsmooth Separable Optimization," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 513-535, March.
    4. 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).
    5. Howard D. Bondell & Brian J. Reich, 2009. "Simultaneous Factor Selection and Collapsing Levels in ANOVA," Biometrics, The International Biometric Society, vol. 65(1), pages 169-177, March.
    6. Hua Zhou & Yichao Wu, 2014. "A Generic Path Algorithm for Regularized Statistical Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 686-699, June.
    7. Aigner, D J & Amemiya, Takeshi & Poirier, Dale J, 1976. "On the Estimation of Production Frontiers: Maximum Likelihood Estimation of the Parameters of a Discontinuous Density Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(2), pages 377-396, June.
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    Cited by:

    1. Cristofari, Andrea, 2023. "A decomposition method for lasso problems with zero-sum constraint," European Journal of Operational Research, Elsevier, vol. 306(1), pages 358-369.

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