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A decomposition method for lasso problems with zero-sum constraint

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  • Cristofari, Andrea

Abstract

In this paper, we consider lasso problems with zero-sum constraint, commonly required for the analysis of compositional data in high-dimensional spaces. A novel algorithm is proposed to solve these problems, combining a tailored active-set technique, to identify the zero variables in the optimal solution, with a 2-coordinate descent scheme. At every iteration, the algorithm chooses between two different strategies: the first one requires to compute the whole gradient of the smooth term of the objective function and is more accurate in the active-set estimate, while the second one only uses partial derivatives and is computationally more efficient. Global convergence to optimal solutions is proved and numerical results are provided on synthetic and real datasets, showing the effectiveness of the proposed method. The software is publicly available.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:306:y:2023:i:1:p:358-369
    DOI: 10.1016/j.ejor.2022.09.030
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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. Andrea Cristofari & Gianni Di Pillo & Giampaolo Liuzzi & Stefano Lucidi, 2022. "An Augmented Lagrangian Method Exploiting an Active-Set Strategy and Second-Order Information," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 300-323, June.
    3. Mishra, Aditya & Müller, Christian L., 2022. "Robust regression with compositional covariates," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).
    4. P. Tseng, 2001. "Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 475-494, June.
    5. 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).
    6. Amir Beck, 2014. "The 2-Coordinate Descent Method for Solving Double-Sided Simplex Constrained Minimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 892-919, September.
    7. Andrea Cristofari, 2019. "An almost cyclic 2-coordinate descent method for singly linearly constrained problems," Computational Optimization and Applications, Springer, vol. 73(2), pages 411-452, June.
    8. Andrea Cristofari & Marianna Santis & Stefano Lucidi & Francesco Rinaldi, 2022. "Minimization over the $$\ell _1$$ ℓ 1 -ball using an active-set non-monotone projected gradient," Computational Optimization and Applications, Springer, vol. 83(2), pages 693-721, November.
    9. Robert Tibshirani & Jacob Bien & Jerome Friedman & Trevor Hastie & Noah Simon & Jonathan Taylor & Ryan J. Tibshirani, 2012. "Strong rules for discarding predictors in lasso‐type problems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(2), pages 245-266, March.
    10. Andrea Cristofari & Marianna Santis & Stefano Lucidi & Francesco Rinaldi, 2020. "An active-set algorithmic framework for non-convex optimization problems over the simplex," Computational Optimization and Applications, Springer, vol. 77(1), pages 57-89, September.
    11. A. Schwartz & E. Polak, 1997. "Family of Projected Descent Methods for Optimization Problems with Simple Bounds," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 1-31, January.
    12. Andrea Cristofari & Marianna Santis & Stefano Lucidi & Francesco Rinaldi, 2017. "A Two-Stage Active-Set Algorithm for Bound-Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 369-401, February.
    13. Patrick L. Combettes & Christian L. Müller, 2021. "Regression Models for Compositional Data: General Log-Contrast Formulations, Proximal Optimization, and Microbiome Data Applications," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(2), pages 217-242, July.
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