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Causal Structure Learning with Conditional and Unique Information Groups-Decomposition Inequalities

Chicharro, D. ORCID: 0000-0002-4038-258X & Nguyen, J. K. (2024). Causal Structure Learning with Conditional and Unique Information Groups-Decomposition Inequalities. Entropy, 26(6), article number 440. doi: 10.3390/e26060440


The causal structure of a system imposes constraints on the joint probability distribution of variables that can be generated by the system. Archetypal constraints consist of conditional independencies between variables. However, particularly in the presence of hidden variables, many causal structures are compatible with the same set of independencies inferred from the marginal distributions of observed variables. Additional constraints allow further testing for the compatibility of data with specific causal structures. An existing family of causally informative inequalities compares the information about a set of target variables contained in a collection of variables, with a sum of the information contained in different groups defined as subsets of that collection. While procedures to identify the form of these groups-decomposition inequalities have been previously derived, we substantially enlarge the applicability of the framework. We derive groups-decomposition inequalities subject to weaker independence conditions, with weaker requirements in the configuration of the groups, and additionally allowing for conditioning sets. Furthermore, we show how constraints with higher inferential power may be derived with collections that include hidden variables, and then converted into testable constraints using data processing inequalities. For this purpose, we apply the standard data processing inequality of conditional mutual information and derive an analogous property for a measure of conditional unique information recently introduced to separate redundant, synergistic, and unique contributions to the information that a set of variables has about a target.

Publication Type: Article
Additional Information: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (
Publisher Keywords: causality; directed acyclic graphs; causal discovery; structure learning; causal structures; marginal scenarios; hidden variables; mutual information; unique information; entropic inequalities; data processing inequality
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments: School of Science & Technology
School of Science & Technology > Computer Science
SWORD Depositor:
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