Definite Non-Ancestral Relations and Structure Learning

TL;DR

This paper introduces a framework for directly learning definite non-ancestral relations in causal DAGs, improving efficiency in structure learning by avoiding initial skeleton discovery.

Contribution

It proposes a novel method to infer non-ancestral relations directly from CPDAGs and d-separation, enhancing causal structure learning algorithms.

Findings

Enables direct inference of non-ancestral relations

Improves efficiency of causal DAG learning algorithms

Provides structural insights without skeleton learning

Abstract

In causal graphical models based on directed acyclic graphs (DAGs), directed paths represent causal pathways between the corresponding variables. The variable at the beginning of such a path is referred to as an ancestor of the variable at the end of the path. Ancestral relations between variables play an important role in causal modeling. In existing literature on structure learning, these relations are usually deduced from learned structures and used for orienting edges or formulating constraints of the space of possible DAGs. However, they are usually not posed as immediate target of inference. In this work we investigate the graphical characterization of ancestral relations via CPDAGs and d-separation relations. We propose a framework that can learn definite non-ancestral relations without first learning the skeleton. This frame-work yields structural information that can be used in both score- and constraint-based algorithms to learn causal DAGs more efficiently.