Restricted Hidden Cardinality Constraints in Causal Models

Beata Zjawin
Elie Wolfe
Robert W. Spekkens

Causal models with unobserved variables impose nontrivial constraints on the distributions over the observed variables. When a common cause of two variables is unobserved, it is impossible to uncover the causal relation between them without making additional assumptions about the model. In this work, we consider causal models with a promise that unobserved variables have known cardinalities. We derive inequality constraints implied by d-separation in such models. Moreover, we explore the possibility of leveraging this result to study causal influence in models that involve quantum systems.

In Chris Heunen and Miriam Backens: Proceedings 18th International Conference on Quantum Physics and Logic (QPL 2021), Gdansk, Poland, and online, 7-11 June 2021, Electronic Proceedings in Theoretical Computer Science 343, pp. 119–131.
Published: 18th September 2021.

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A post-publication revision appears at arXiv. Two references have been added.
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