Causal Networks: Semantics and Expressiveness
This work addresses foundational issues in causal inference and graphical models for researchers in statistics and machine learning, but it appears incremental as it builds on existing graphoid axioms and d-separation concepts.
The paper tackled the problem of representing dependency knowledge efficiently using graphical structures, showing that d-separation is a sound rule for reading independencies from directed acyclic graphs (DAGs) based on causal input lists from graphoids, and extended it to cover functional and conditional dependencies.
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.