Learning from Pairwise Marginal Independencies
This work addresses the challenge of causal inference for researchers in statistics and machine learning by providing foundational insights into model space mapping, though it appears incremental as it builds on existing independence-based methods.
The paper tackles the problem of characterizing and enumerating directed acyclic graphs (DAGs) that faithfully explain pairwise marginal independencies, such as zero entries in a covariance matrix, and shows the extent to which causal inference can be performed without conditional independence tests.
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.