Efficiently Deciding Algebraic Equivalence of Bow-Free Acyclic Path Diagrams
This work addresses a bottleneck in causal discovery for researchers dealing with latent variables, though it is incremental as it builds on known algebraic constraints in a specific model.
The paper tackles the problem of distinguishing causal graphs with latent confounders by studying algebraic constraints in linear structural equation models without bows, proposing efficient algorithms to decide algebraic equivalence and subset relationships between graphs.
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.