aiqbench analysis
This research establishes a complete characterization of observational dominance for causal structures with latent variables, demonstrating that nontrivial inequality constraints—and thus potential quantum-classical gaps—are ubiquitous as system complexity increases. The findings suggest that standard constraint-based causal discovery algorithms relying solely on conditional independence are insufficient, highlighting the necessity for methods incorporating nested Markov and inequality constraints to distinguish between classical and quantum realizable distributions.
The observational partial order of causal structures with latent variables
arXiv:2502.07891v3 Announce Type: replace-cross Abstract: For two causal structures with the same set of visible variables, one is said to observationally dominate the other if the set of distributions over the visible variables realizable by the first contains the set of distributions over the visible variables realizable by the second. Knowing such dominance relations is useful for adjudicating between these structures given observational data. Here, we consider the problem of determining the partial order of equivalence classes of causal structures with latent variables relative to observational dominance. We provide a complete characterization of the dominance order in the case of three visible variables, and a partial characterization in the case of four visible variables. Our techniques also help to identify which observational equivalence classes have a set of realizable distributions that is characterized by nontrivial inequality constraints, analogous to Bell inequalities and instrumental inequalities. We find evidence that as one increases the number of visible variables, the equivalence classes satisfying nontrivial inequality constraints become ubiquitous. (Because such classes are the ones for which there can be a difference in the distributions that are quantumly and classically realizable, this implies that the potential for quantum-classical gaps is also ubiquitous.) Furthermore, we find evidence that constraint-based causal discovery algorithms that rely solely on conditional independence constraints have a significantly weaker distinguishing power among observational equivalence classes than algorithms that go beyond these (i.e., algorithms that also leverage nested Markov constraints and inequality constraints).
Abstract:For two causal structures with the same set of visible variables, one is said to observationally dominate the other if the set of distributions over the visible variables realizable by the first contains the set of distributions over the visible variables realizable by the second. Knowing such dominance relations is useful for adjudicating between these structures given observational data. Here, we consider the problem of determining the partial order of equivalence classes of causal structures with latent variables relative to observational dominance. We provide a complete characterization of the dominance order in the case of three visible variables, and a partial characterization in the case of four visible variables. Our techniques also help to identify which observational equivalence classes have a set of realizable distributions that is characterized by nontrivial inequality constraints, analogous to Bell inequalities and instrumental inequalities. We find evidence that as one increases the number of visible variables, the equivalence classes satisfying nontrivial inequality constraints become ubiquitous. (Because such classes are the ones for which there can be a difference in the distributions that are quantumly and classically realizable, this implies that the potential for quantum-classical gaps is also ubiquitous.) Furthermore, we find evidence that constraint-based causal discovery algorithms that rely solely on conditional independence constraints have a significantly weaker distinguishing power among observational equivalence classes than algorithms that go beyond these (i.e., algorithms that also leverage nested Markov constraints and inequality constraints).
48 pages, 30 figures; changes following referee reviews. The most significant changes are the text in Sections 3.4 and 7.2, fixes to the statements of Propositions 7 and 8 and to the proof of Lemma 10, and the removal of the previous Proposition 3
Machine Learning (stat.ML); Machine Learning (cs.LG); Quantum Physics (quant-ph)
arXiv:2502.07891 [stat.ML]
(or arXiv:2502.07891v3 [stat.ML] for this version)
Journal of Causal Inference,vol.14, no.1, 2026, pp.20250009
https://doi.org/10.1515/jci-2025-0009 DOI(s) linking to related resources
Full text under the publisher's open licence · 310 words
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