2021/08/06 by Jean‐Philippe Chancelier, Chancelier, Jean-Philippe, Michel De Lara +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Causal Inference Techniques #Advanced Data Processing Techniques #Arithmetic #Bayesian Modeling and Causal Inference #Binary number #Combinatorics #Computer science #Conditional independence #Data mining #Directed acyclic graph #Discrete Mathematics (cs.DM) #Discrete mathematics #FOS: Computer and information sciences #Independence (probability theory) #Mathematics #Pearl #Philosophy #Relation (database) #Separation (statistics) #Statistical Methods and Inference #Statistics
paper · pdf · open access · doi:10.48550/arxiv.2108.03018
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2021/08/06 · openalex created_date 2022/09/30 · openalex updated_date 2026/08/05
The concept of d-separation holds a pivotal role in causality theory, serving as a fundamental tool for deriving conditional independence properties from causal graphs. Pearl defined the d-separation of two subsets conditionally on a third one. In this study, we present a novel perspective by showing i) how the d-separation can be extended beyond acyclic graphs, possibly infinite, and ii) how it can be expressed and characterized as a binary relation between vertices. Compared to the typical perspectives in causality theory, our equivalence opens the door to more compact and computational proofing techniques, because the language of binary relations is well adapted to equational reasoning. Additionally, and of independent interest, the proofs of the results presented in this paper are checked with the Coq proof assistant.