Restricted Hidden Cardinality Constraints in Causal Models
Statistics Theory
2021-12-14 v2 Quantum Physics
Machine Learning
Statistics Theory
Abstract
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.
Cite
@article{arxiv.2109.05656,
title = {Restricted Hidden Cardinality Constraints in Causal Models},
author = {Beata Zjawin and Elie Wolfe and Robert W. Spekkens},
journal= {arXiv preprint arXiv:2109.05656},
year = {2021}
}
Comments
This is a revision of a paper with the same title, published in EPTCS 343, 2021, pp. 119-131, arXiv:2109.05656v1. Two references have been added