Efficiently Deciding Algebraic Equivalence of Bow-Free Acyclic Path Diagrams

TL;DR

This paper introduces efficient algorithms to determine whether two bow-free acyclic path diagrams impose the same or subset algebraic constraints, advancing causal discovery in models with latent confounders.

Contribution

It presents novel algorithms for deciding algebraic equivalence of bow-free acyclic path diagrams, enhancing causal discovery methods.

Findings

Algorithms efficiently decide algebraic constraint equivalence.

Algebraic constraints provide fine-grained causal graph resolution.

Improves understanding of constraints beyond conditional independences.

Abstract

For causal discovery in the presence of latent confounders, constraints beyond conditional independences exist that can enable causal discovery algorithms to distinguish more pairs of graphs. Such constraints are not well-understood yet. In the setting of linear structural equation models without bows, we study algebraic constraints and argue that these provide the most fine-grained resolution achievable. We propose efficient algorithms that decide whether two graphs impose the same algebraic constraints, or whether the constraints imposed by one graph are a subset of those imposed by another graph.