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Structure learning of sparse directed acyclic graphs incorporating the scale-free property

Author

Listed:
  • Xiao Guo

    (Northwest University)

  • Hai Zhang

    (Northwest University
    Macau University of Science and Technology)

  • Yao Wang

    (Xi’an Jiaotong University)

  • Yong Liang

    (Macau University of Science and Technology)

Abstract

Directed acyclic graphs have been widely used to model the causal relationships among variables. Many existing works focus on $$l_1$$ l 1 based methods to induce sparsity. However, in addition to sparsity, studies on networks show that many real networks are scale-free, that is, the degree of the network follows a power-law. To capture the scale-free property, in this paper we propose a novel penalized likelihood method by employing a log 1-norm group penalty which is the composite of the well-known log-type and lasso-type penalty functions. We then design an efficient coordinate descent algorithm to solve the resulting nonconvex problem. Moreover, we establish the estimation consistency of the estimator under the setting where the error variances are fixed at an identical constant. Numerical studies are also conducted to demonstrate the merits of our method.

Suggested Citation

  • Xiao Guo & Hai Zhang & Yao Wang & Yong Liang, 2019. "Structure learning of sparse directed acyclic graphs incorporating the scale-free property," Computational Statistics, Springer, vol. 34(2), pages 713-742, June.
    • Handle: RePEc:spr:compst:v:34:y:2019:i:2:d:10.1007_s00180-018-0841-8
    DOI: 10.1007/s00180-018-0841-8
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    References listed on IDEAS

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    4. Fei Fu & Qing Zhou, 2013. "Learning Sparse Causal Gaussian Networks With Experimental Intervention: Regularization and Coordinate Descent," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 288-300, March.
    5. Ali Shojaie & George Michailidis, 2010. "Penalized likelihood methods for estimation of sparse high-dimensional directed acyclic graphs," Biometrika, Biometrika Trust, vol. 97(3), pages 519-538.
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