Structural learning of simple staged trees

• Published in: Data mining and knowledge discovery Vol. 38; no. 3; pp. 1520 - 1544
• Main Authors: Leonelli, Manuele, Varando, Gherardo
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.05.2024; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Bayesian analysis; Chemistry and Earth Sciences; Computer Science; Data Mining and Knowledge Discovery; Graph coloring; Independence; Information Storage and Retrieval; Machine learning; Networks; Physics; Random variables; Statistics for Engineering; Context-specific independence; Bayesian networks; Staged trees; Structural learning; Asymmetric graphical models
• ISSN: 1384-5810; 1573-756X
• DOI: 10.1007/s10618-024-01007-0

Bayesian networks faithfully represent the symmetric conditional independences existing between the components of a random vector. Staged trees are an extension of Bayesian networks for categorical random vectors whose graph represents non-symmetric conditional independences via vertex coloring. However, since they are based on a tree representation of the sample space, the underlying graph becomes cluttered and difficult to visualize as the number of variables increases. Here, we introduce the first structural learning algorithms for the class of simple staged trees, entertaining a compact coalescence of the underlying tree from which non-symmetric independences can be easily read. We show that data-learned simple staged trees often outperform Bayesian networks in model fit and illustrate how the coalesced graph is used to identify non-symmetric conditional independences.