Efficiently Deciding Algebraic Equivalence of Bow-Free Acyclic Path Diagrams
<|reference_start|>Efficiently Deciding Algebraic Equivalence of Bow-Free Acyclic Path Diagrams: 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.<|reference_end|>
@article{van ommen2024efficiently,
    title={Efficiently Deciding Algebraic Equivalence of Bow-Free Acyclic Path
  Diagrams},
    author={Thijs van Ommen},
    journal={arXiv preprint arXiv:2406.09049},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.09049},
    primaryClass={cs.LG math.ST stat.ML stat.TH}
}