Reasoning about Independence in Probabilistic Models of Relational Data

TL;DR

This paper extends d-separation to relational data, introducing relational d-separation and abstract ground graphs to accurately infer conditional independence in complex probabilistic models.

Contribution

It develops a new theory and representation for reasoning about independence in relational probabilistic models, improving accuracy and efficiency.

Findings

Relational d-separation accurately infers conditional independence.

Abstract ground graphs enable sound and complete reasoning.

Empirical results demonstrate the method's effectiveness.

Abstract

We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data inaccurately infers conditional independence. We introduce relational d-separation, a theory for deriving conditional independence facts from relational models. We provide a new representation, the abstract ground graph, that enables a sound, complete, and computationally efficient method for answering d-separation queries about relational models, and we present empirical results that demonstrate effectiveness.