Local Characterizations of Causal Bayesian Networks
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.
KeywordsDirected Acyclic Graph Probabilistic Interpretation Manipulate Variable Interventional Distribution Causal Information
Unable to display preview. Download preview PDF.
- 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
- Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. MIT Press (2009)Google Scholar
- Lauritzen, S.L.: Graphical Models. Clarendon Press, Oxford (1996)Google Scholar
- Lauritzen, S.L.: Causal inference from graphical models. In: Complex Stochastic Systems, pp. 63–107. Chapman and Hall/CRC Press (1999)Google Scholar
- 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
- Pearl, J.: Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, San Mateo (1988)Google Scholar
- 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
- 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
- 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