Latent free equivalent mDAGs

Evans, Robin J.

doi:10.2140/astat.2023.14.3

Cited by 1 publication

(1 citation statement)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The availability of inequalities easily derived by reading the original causal structure can also be helpful in combination with the inflation method, in order to discard as many candidate causal structures as possible before the design of additional inflated graphs. The connection with other approaches [ 69 , 70 , 71 , 72 , 73 , 74 ] also deserves further investigation, ultimately to determine minimal sets of inequality constraints with equivalent inferential power.…”

Section: Discussionmentioning

confidence: 99%

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

Chicharro,

Nguyen

2024

Entropy

View full text Add to dashboard Cite

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.

show abstract