Local Characterizations of Causal Bayesian Networks

  • Elias Bareinboim
  • Carlos Brito
  • Judea Pearl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7205)


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.


Directed Acyclic Graph Probabilistic Interpretation Manipulate Variable Interventional Distribution Causal Information 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Dawid, A.P.: Influence diagrams for causal modelling and inference. International Statistical Review 70(2), 161–189 (2001)CrossRefGoogle Scholar
  2. Galles, D., Pearl, J.: An axiomatic characterization of causal counterfactuals. Foundation of Science 3(1), 151–182 (1998)MathSciNetCrossRefGoogle Scholar
  3. Geiger, D., Verma, T.S., Pearl, J.: Identifying independence in Bayesian networks. Networks 20, 507–534 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  4. Halpern, J.Y.: Axiomatizing causal reasoning. In: Cooper, G.F., Moral, S. (eds.) Uncertainty in Artificial Intelligence, pp. 202–210. Morgan Kaufmann, San Francisco (1998); Also, Journal of Artificial Intelligence Research 12(3), 17–37 (2000)Google Scholar
  5. Heckerman, D., Shachter, R.: Decision-theoretic foundations for causal reasoning. Journal of Artificial Intelligence Research 3, 405–430 (1995)zbMATHGoogle Scholar
  6. Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. MIT Press (2009)Google Scholar
  7. Lauritzen, S.L.: Graphical Models. Clarendon Press, Oxford (1996)Google Scholar
  8. Lauritzen, S.L.: Causal inference from graphical models. In: Complex Stochastic Systems, pp. 63–107. Chapman and Hall/CRC Press (1999)Google Scholar
  9. Lindley, D.V.: Seeing and doing: The concept of causation. International Statistical Review 70, 191–214 (2002)zbMATHCrossRefGoogle Scholar
  10. Pearl, J., Verma, T.: The logic of representing dependencies by directed acyclic graphs. In: Proceedings of the Sixth National Conference on AI (AAAI 1987), Seattle, WA, pp. 374–379 (July 1987)Google Scholar
  11. Pearl, J.: Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, San Mateo (1988)Google Scholar
  12. Pearl, J.: Belief networks revisited. Artificial Intelligence 59, 49–56 (1993)CrossRefGoogle Scholar
  13. Pearl, J.: A probabilistic calculus of actions. In: Lopez de Mantaras, R., Poole, D. (eds.) Uncertainty in Artificial Intelligence 10, pp. 454–462. Morgan Kaufmann, San Mateo (1994)Google Scholar
  14. Pearl, J.: Causality: Models, Reasoning, and Inference. Cambridge University Press, New York (2000); 2nd edn. (2009)zbMATHGoogle Scholar
  15. Pearl, J.: Causality: Models, Reasoning, and Inference, 2nd edn. Cambridge University Press, New York (2009)zbMATHGoogle Scholar
  16. Robins, J.M.: A new approach to causal inference in mortality studies with a sustained exposure period – applications to control of the healthy workers survivor effect. Mathematical Modeling 7, 1393–1512 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  17. Spirtes, P., Glymour, C.N., Scheines, R.: Causation, Prediction, and Search. Springer, New York (1993)zbMATHCrossRefGoogle Scholar
  18. Tian, J., Pearl, J.: A new characterization of the experimental implications of causal Bayesian networks. In: Proceedings of the Eighteenth National Conference on Artificial Intelligence, pp. 574–579. AAAI Press/The MIT Press, Menlo Park, CA (2002)Google Scholar
  19. Tian, J., Kang, C., Pearl, J.: A characterization of interventional distributions in semi-Markovian causal models. In: Proceedings of the Twenty-First National Conference on Artificial Intelligence, pp. 1239–1244. AAAI Press, Menlo Park (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Elias Bareinboim
    • 1
  • Carlos Brito
    • 2
  • Judea Pearl
    • 1
  1. 1.Cognitive Systems Laboratory, Computer Science DepartmentUniversity of CaliforniaLos AngelesUSA
  2. 2.Computer Science DepartmentFederal University of CearáBrazil

Personalised recommendations