Causal networks: semantics and expressiveness

By Thomas Verma, Judea Pearl. 2013

572 citations recorded by the source corpus.

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 graphical structures such as undirected graphs and directed acyclic graphs (DAGs). In this paper we show that the graphical criterion called d-separation is a sound rule for reading independencies from any DAG based on a causal input list drawn from a graphoid. The rule may be extended to cover DAGs that represent functional dependencies as well as conditional dependencies.

Subfields: Artificial Intelligence, Signal Processing

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Citations in the corpus

Causal Markov condition for submodular information measures (2010, methodology): “n-descendants of a node ared-separated from the node itself by the parents. (1) →(3). Since the dependence measure I satisﬁes the graphoid axioms (Lemma 4) we can apply Theorem 2 in Verma & Pearl [25] which asserts that the DAG is an I-map, or in other words that d-separation relations represent”
Bayesian Networks (2008, unknown): “In fact, any independence statement derived this way can be read off the Bayesian network structure using a graphical criterion known as d-separation [166] [35] [64].”
FUNDAMENTALS OF STATISTICAL CAUSALITY (2007, background): “However there is an alternative formulation that is commonly seen, based on the property of d-separation (Pearl 1986; Verma and Pearl 1990).”
Equivalence and Synthesis of Causal Models (1990, background): “…and Matheson 81] [Olmsted 84] and [Shachter 85] and evidential reasoning [Pearl 88], and has also received extensive theoretical studies [Geiger and Pearl 90], [Geiger et al 90], [Glymour et al 1987], [Pearl and Verma 87], [Shachter 85], [Smith 89], [Spirtes et al 90] and [Verma and Pearl 90].”
Structure Learning in Graphical Modeling (2016, background): “Then the distribution of X factorizes according to a DAG G = ( V, E ) if it has a density of the form The global and local Markov properties are equivalent, and under the assumed existence of a density they are equivalent to the factorization property (Verma & Pearl, 1988).”
Minimal sufficient causation and directed acyclic graphs (2009, background): “It has been shown that if all paths between A and B are blocked given Z, then A and B are conditionally independent given Z [8, 13, 40].”
Statistical Causality from a Decision-Theoretic Perspective (2014, background): “…by the values of X3 (properties of the suspect’s jumper) and of A (an indicator of whether or not the fibres came from 9The name refers to an alternative, but equivalent, way of expressing this separation property, as described by Pearl (1986); Verma and Pearl (1990). the suspect’s jumper).”
A New Inferential Test for Path Models Based on Directed Acyclic Graphs (2000, methodology): “The test is based on the notion of d-separation of vertices in a DAG (Verma & Pearl 1988).”
Causal Inference from Graphical Models (2001, methodology): “It was shown in Verma and Pearl (1990) that Lemma 1.10 For any xed directed acyclic graph D, the relation ?”
Graphical methods for inequality constraints in marginalized DAGs (2012, methodology): “It is well known that d-separation is equivalent to the factorization criterion Verma and Pearl (1988).”
Multi-Agent Influence Diagrams for Representing and Solving Games (2001, background): “As shown by Verma and Pearl [ 36 ], d-separation is sound: d-separation in G implies conditional independence for any Bayesian networkB = (G; Pr).”