On the Relationship between Bayesian Networks and Probabilistic Structural Causal Models

TL;DR

This paper explores the connection between Bayesian networks and structural causal models, analyzing how one can be transformed into the other and the implications for their semantics.

Contribution

It demonstrates how linear algebra and linear programming facilitate the transformation from Bayesian networks to probabilistic structural causal models.

Findings

Linear algebra and linear programming are key tools for transformation.

Conditions for existence and uniqueness of solutions are analyzed.

The impact on model semantics is examined.

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.