Causal Networks: Semantics and Expressiveness

TL;DR

This paper explores the semantics and expressiveness of causal networks, demonstrating how d-separation can reliably infer independencies in DAGs based on graphoid axioms, including extensions to functional dependencies.

Contribution

It establishes that d-separation is a sound criterion for reading independencies from DAGs derived from causal input lists, broadening its applicability.

Findings

d-separation is a sound rule for reading independencies

Extensions cover DAGs representing functional dependencies

Graphical structures efficiently represent dependency knowledge

Abstract

Dependency knowledge of the form "x is independent of y once z is known" invariably obeys the four graphoid axioms, examples include probabilistic and database dependencies. Often, such knowledge can be represented efficiently with graphical structures such as undirected graphs and directed acyclic graphs (DAGs). In this paper we show that the graphical criterion called d-separation is a sound rule for reading independencies from any DAG based on a causal input list drawn from a graphoid. The rule may be extended to cover DAGs that represent functional dependencies as well as conditional dependencies.