City Research Online

Abstract

The joint probability distribution of observable variables from a system is constrained by the underlying causal structure. In the presence of hidden variables, untestable independencies that involve hidden variables lead to testable causally-imposed inequality constraints for observable variables, whose violation can reject the compatibility of a causal structure with data. One type of causally informative inequalities is entropic inequalities, which appear in the space of entropic terms associated with the distribution of observable variables. We derive a new type of minimum information (minInf) entropic inequalities that substantially increases causal inference power. These new entropic inequalities appear when considering the constraints that the causal structure imposes on entropic terms determined by information minimization within families of distributions that preserve sets of marginals shared with the original distribution. We introduce a new family of minInf data processing inequalities and a procedure to recursively combine different types of data processing inequalities to create tighter testable entropic inequalities. We extensively illustrate the applicability of this procedure in the instrumental causal scenario, integrating the new inequalities with standard instrumental entropic inequalities constructed with multivariate instrumental sets. We also provide additional examples with other types of entropic inequalities, such as the Information Causality and Groups-Decomposition inequalities.

Publication Type:	Article
Additional Information:	© The Authors. Published by MDPI. This is an open-access article distributed under the terms of Creative Commons: Attribution International Public License 4.0 (http://creativecommons.org/licenses/by/4.0/).
Publisher Keywords:	causality; directed acyclic graphs; causal discovery; structure learning; marginal scenarios; hidden variables; mutual information; entropic inequalities; data processing inequalities; maximum entropy; minimum information; instrumental inequality; shannon entropy cone; information causality
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology School of Science & Technology > Department of Computer Science
SWORD Depositor:	Symplectic Administrator

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