Learning from Pairwise Marginal Independencies

TL;DR

This paper characterizes DAGs that explain pairwise marginal independencies among variables, providing algorithms to enumerate such structures and exploring the limits of causal inference without conditional independence tests.

Contribution

It introduces a characterization of faithful DAGs for pairwise marginal independencies and develops algorithms for their enumeration, advancing causal model understanding.

Findings

Mapped the space of faithful causal models for given independencies

Provided algorithms for efficient enumeration of DAGs

Showed causal inference possibilities without conditional independence tests

Abstract

We consider graphs that represent pairwise marginal independencies amongst a set of variables (for instance, the zero entries of a covariance matrix for normal data). We characterize the directed acyclic graphs (DAGs) that faithfully explain a given set of independencies, and derive algorithms to efficiently enumerate such structures. Our results map out the space of faithful causal models for a given set of pairwise marginal independence relations. This allows us to show the extent to which causal inference is possible without using conditional independence tests.