🤖 AI Summary
This study investigates whether Bayesian networks can be mapped to probabilistic structural causal models (SCMs) and analyzes the implications of such a mapping for network structure and joint distributions. By introducing independent latent random variables, deterministic structural equations are extended into probabilistic form, establishing correspondences between the two frameworks at semantic, structural, and distributional levels. Leveraging tools from linear algebra and linear programming, the work formulates criteria for the existence and uniqueness of such model transformations, revealing how these conditions depend on model dimensionality. The analysis further elucidates the theoretical consequences of the transformation for causal semantics and the resulting probability distributions.
📝 Abstract
In this paper, the relationship between probabilistic graphical models, in particular Bayesian networks, and causal diagrams, also called structural causal models, is studied. Structural causal models are deterministic models, based on structural equations or functions, that can be provided with uncertainty by adding independent, unobserved random variables to the models, equipped with probability distributions. One question that arises is whether a Bayesian network that has obtained from expert knowledge or learnt from data can be mapped to a probabilistic structural causal model, and whether or not this has consequences for the network structure and probability distribution. We show that linear algebra and linear programming offer key methods for the transformation, and examine properties for the existence and uniqueness of solutions based on dimensions of the probabilistic structural model. Finally, we examine in what way the semantics of the models is affected by this transformation.
Keywords: Causality, probabilistic structural causal models, Bayesian networks, linear algebra, experimental software.