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Pearl's d-separation is a foundational notion to study conditional independence between random variables. We define the topological conditional separation and we show that it is equivalent to the d-separation, extended beyond acyclic…
We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data…
The d-separation criterion detects the compatibility of a joint probability distribution with a directed acyclic graph through certain conditional independences. In this work, we study this problem in the context of categorical probability…
The design of scientific experiments deserves its own variation of formal verification to catch cases where scientists made important mistakes, such as forgetting to take confounding variables into account. One of the most fundamental…
We show that the d -separation criterion constitutes a valid test for conditional independence relationships that are induced by feedback systems involving discrete variables.
The rules of d-separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d-separation, a theory for…
Pearl and Dechter (1996) claimed that the d-separation criterion for conditional independence in acyclic causal networks also applies to networks of discrete variables that have feedback cycles, provided that the variables of the system are…
Among Judea Pearl's many contributions to Causality and Statistics, the graphical d-separation} criterion, the do-calculus and the mediation formula stand out. In this chapter we show that d-separation} provides direct insight into an…
Spirtes, Glymour and Scheines formulated a Conjecture that a direct dependence test and a head-to-head meeting test would suffice to construe directed acyclic graph decompositions of a joint probability distribution (Bayesian network) for…
The assumed causal relationships depicted in a DAG are interpreted using a set of rules called D-separation rules. Although these rules can be implemented automatically using standard software, at least a basic understanding of their…
A causal model is an abstract representation of a physical system as a directed acyclic graph (DAG), where the statistical dependencies are encoded using a graphical criterion called `d-separation'. Recent work by Wood & Spekkens shows that…
Pearl and Verma developed d-separation as a widely used graphical criterion to reason about the conditional independencies that are implied by the causal structure of a Bayesian network. As acyclic ground probabilistic logic programs…
Inferring the potential consequences of an unobserved event is a fundamental scientific question. To this end, Pearl's celebrated do-calculus provides a set of inference rules to derive an interventional probability from an observational…
Causal modelling frameworks link observable correlations to causal explanations, which is a crucial aspect of science. These models represent causal relationships through directed graphs, with vertices and edges denoting systems and…
We present a definition of cause and effect in terms of decision-theoretic primitives and thereby provide a principled foundation for causal reasoning. Our definition departs from the traditional view of causation in that causal assertions…
This paper explores the role of Directed Acyclic Graphs (DAGs) as a representation of conditional independence relationships. We show that DAGs offer polynomially sound and complete inference mechanisms for inferring conditional…
A fundamental challenge in the empirical sciences involves uncovering causal structure through observation and experimentation. Causal discovery entails linking the conditional independence (CI) invariances in observational data to their…
Dependency knowledge of the form "x is independent of y once z is known" invariably obeys the four graphoid axioms, examples include probabilistic and database dependencies. Often, such knowledge can be represented efficiently with…
Pearls concept OF a d - connecting path IS one OF the foundations OF the modern theory OF graphical models : the absence OF a d - connecting path IN a DAG indicates that conditional independence will hold IN ANY distribution factorising…
We propose a new approach to temporal inference, inspired by the Pearlian causal inference paradigm - though quite different from Pearl's approach formally. Rather than using directed acyclic graphs, we make use of factored sets, which are…