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Densely connected sub-Gaussian linear structural equation model learning via ℓ1- and ℓ2-regularized regressions

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  • Choi, Semin
  • Kim, Yesool
  • Park, Gunwoong

Abstract

This paper develops a new algorithm for learning densely connected sub-Gaussian linear structural equation models (SEMs) in high-dimensional settings, where the number of nodes increases with increasing number of samples. The proposed algorithm consists of two main steps: (i) the component-wise ordering estimation using ℓ2-regularized regression and (ii) the presence of edge estimation using ℓ1-regularized regression. Hence, the proposed algorithm can recover a large degree graph with a small indegree constraint. Also proven is that the sample size n=Ω(p) is sufficient for the proposed algorithm to recover a sub-Gaussian linear SEM provided that d=O(plog⁡p), where p is the number of nodes and d is the maximum indegree. In addition, the computational complexity is polynomial, O(np2max⁡(n,p)). Therefore, the proposed algorithm is statistically consistent and computationally feasible for learning a densely connected sub-Gaussian linear SEM with large maximum degree. Numerical experiments verified that the proposed algorithm is consistent, and performs better than the state-of-the-art high-dimensional linear SEM learning HGSM, LISTEN, and TD algorithms in both sparse and dense graph settings. Also demonstrated through real data is that the proposed algorithm is well-suited to estimating the Seoul public bike usage patterns in 2019.

Suggested Citation

  • Choi, Semin & Kim, Yesool & Park, Gunwoong, 2023. "Densely connected sub-Gaussian linear structural equation model learning via ℓ1- and ℓ2-regularized regressions," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:csdana:v:181:y:2023:i:c:s0167947323000026
    DOI: 10.1016/j.csda.2023.107691
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