The m-connecting imset and factorization for ADMG models

TL;DR

This paper introduces the m-connecting imset and factorization criterion for ADMG models, providing new statistical tools that facilitate learning and inference in systems with latent confounding, addressing limitations of DAG models.

Contribution

The paper presents the m-connecting imset and a single-equation factorization criterion for ADMGs, establishing their equivalence to the global Markov property and enhancing statistical analysis tools.

Findings

Introduced the m-connecting imset for ADMGs

Defined the m-connecting factorization criterion and proved its equivalence to the global Markov property

Formulated a consistent scoring criterion with a closed-form solution

Abstract

Directed acyclic graph (DAG) models have become widely studied and applied in statistics and machine learning -- indeed, their simplicity facilitates efficient procedures for learning and inference. Unfortunately, these models are not closed under marginalization, making them poorly equipped to handle systems with latent confounding. Acyclic directed mixed graph (ADMG) models characterize margins of DAG models, making them far better suited to handle such systems. However, ADMG models have not seen wide-spread use due to their complexity and a shortage of statistical tools for their analysis. In this paper, we introduce the m-connecting imset which provides an alternative representation for the independence models induced by ADMGs. Furthermore, we define the m-connecting factorization criterion for ADMG models, characterized by a single equation, and prove its equivalence to the global Markov property. The m-connecting imset and factorization criterion provide two new statistical tools for learning and inference with ADMG models. We demonstrate the usefulness of these tools by formulating and evaluating a consistent scoring criterion with a closed form solution.