On the Logic of Causal Models
This work addresses foundational issues in causal modeling and inference for researchers in statistics and machine learning, but it appears incremental as it builds on existing graphical criteria and properties.
The paper tackles the problem of representing conditional independence relationships using Directed Acyclic Graphs (DAGs), showing that DAGs provide polynomially sound and complete inference mechanisms and that d-separation uncovers more valid independencies than any other criterion.
This paper explores the role of Directed Acyclic Graphs (DAGs) as a representation of conditional independence relationships. We show that DAGs offer polynomially sound and complete inference mechanisms for inferring conditional independence relationships from a given causal set of such relationships. As a consequence, d-separation, a graphical criterion for identifying independencies in a DAG, is shown to uncover more valid independencies then any other criterion. In addition, we employ the Armstrong property of conditional independence to show that the dependence relationships displayed by a DAG are inherently consistent, i.e. for every DAG D there exists some probability distribution P that embodies all the conditional independencies displayed in D and none other.