Local characterizations of causal bayesian networks

Authors:
Elias Bareinboim;Carlos Brito;Judea Pearl
Affiliations:
Cognitive Systems Laboratory, Computer Science Department, University of California, Los Angeles, CA;Computer Science Department, Federal University of Ceará, Brazil;Cognitive Systems Laboratory, Computer Science Department, University of California, Los Angeles, CA
Venue:
GKR'11 Proceedings of the Second international conference on Graph Structures for Knowledge Representation and Reasoning
Year:
2011

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Abstract

The standard definition of causal Bayesian networks (CBNs) invokes a global condition according to which the distribution resulting from any intervention can be decomposed into a truncated product dictated by its respective mutilated subgraph. We analyze alternative formulations which emphasizes local aspects of the causal process and can serve therefore as more meaningful criteria for coherence testing and network construction. We first examine a definition based on "modularity" and prove its equivalence to the global definition. We then introduce two new definitions, the first interprets the missing edges in the graph, and the second interprets "zero direct effect" (i.e., ceteris paribus). We show that these formulations are equivalent but carry different semantic content.