Efficiently Deciding Algebraic Equivalence of Bow-Free Acyclic Path Diagrams

Thijs van Ommen

Keywords: mixed graphs, latent confounders, algebraic models

TL;DR: We propose an efficient algorithm that tells us if two graphs impose the same algebraic (e.g. Verma) constraints

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.

List Of Authors: van Ommen, Thijs

Code Url: https://github.com/UtrechtUniversity/aelsem_decide

Submission Number: 780