Identifiability of Boolean graphical models

Music City Center 

Boolean graphical models-including prominent subfamilies such as cognitive diagnosis models and Boolean matrix decompositions-find broad applications from social sciences to engineering. Despite their flexibility, a key challenge lies in establishing the identifiability of their graphical structures, which determine how latent variables affect observed data. Existing work often relies on the strong assumption of pure nodes-observed variables that depend directly on only one latent variable. While mathematically convenient, these assumptions may be unrealistic in many real-world settings. To address this, we develop a novel graphical approach using Hasse diagrams, which transforms the identifiability problem into a graph isomorphism challenge. Building on this perspective, we propose sufficient and necessary conditions for identifiability that do not require pure nodes; rather, the graphical structure is identifiable precisely when the corresponding graphical representation is unique.

Identifiability

Boolean graphical models

Graphical structures

Boolean matrix decomposition

Cognitive diagnosis models

Hasse diagrams 

Section on Statistical Learning and Data Science