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

Semin Choi, Yesool Kim and Gunwoong Park

Computational Statistics & Data Analysis, 2023, vol. 181, issue C

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.

Keywords: Bayesian networks; Causal structure; Directed acyclic graph; Structural equation model; Regularized regression (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947323000026
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:181:y:2023:i:c:s0167947323000026

DOI: 10.1016/j.csda.2023.107691

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().