{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T13:22:39Z","timestamp":1787664159925,"version":"build-2736575974"},"reference-count":43,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T00:00:00Z","timestamp":1787616000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Bayesian Network (BN) learning algorithms may exhibit substantially different performance across graph structures, sample sizes, and evaluation criteria. Comparative evidence on BN learning under structurally validated conditions remains limited. This study evaluates BN learning algorithms for causal discovery through a simulation-based framework that integrates multiple graph structures, sample sizes, and structural equation modeling (SEM)-based validation within a common design. Fourteen constraint-based, score-based, and hybrid algorithms were examined across five randomly generated directed acyclic graphs (DAGs) containing latent constructs and four sample sizes (n = 200, 500, 1000, and 2500). For each DAG\u2013sample size combination, 1000 datasets were generated and validated using SEM, yielding 20,000 accepted datasets. Performance was assessed primarily by Matthews correlation coefficient (MCC), supported by directed structural Hamming distance (SHD) and F1. The results reveal substantial variation across DAG structures, sample sizes, and evaluation metrics, with mean MCC ranging from \u22120.43 to 0.65. Peter\u2013Clark Stable achieved the strongest performance in several conditions, whereas hybrid algorithms were frequently among the weaker performers. Increasing sample size did not produce uniform performance gains, and no algorithm or algorithm class consistently dominated across all settings. These findings show that BN structure learning performance is strongly structure- and condition-dependent and support evaluation across multiple controlled DAG configurations.<\/jats:p>","DOI":"10.3390\/e28090955","type":"journal-article","created":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T12:57:17Z","timestamp":1787662637000},"page":"955","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Performance Evaluation of Bayesian Network Learning Algorithms in Structural Equation Modeling: A Simulation Study"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3579-7764","authenticated-orcid":false,"given":"Tugay","family":"Karadag","sequence":"first","affiliation":[{"name":"Department of Statistics, Yildiz Technical University, Istanbul 32220, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,25]]},"reference":[{"key":"ref_1","first-page":"8","article-title":"Causal-learn: Causal discovery in Python","volume":"25","author":"Zheng","year":"2024","journal-title":"J. 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