A Bayesian Approach to Learning Causal networks

1. A Bayesian Approach to Learning Causal networks David Heckerman Haimonti Dutta, Department Of Computer and Information Science

2. Objectives • Showing that causal networks are different from a causal ones • Identification of circumstances in which methods for learning acausal networks are applicable to learning causal networks Haimonti Dutta, Department Of Computer and Information Science

3. A Causal Network is…… A directed acyclic graph where Nodes correspond to chance variables in U Non root node is a direct causal effect of its parents. Haimonti Dutta, Department Of Computer and Information Science

4. f b m Causal Bayesian Networks and Influence diagrams A Causal Network : s Haimonti Dutta, Department Of Computer and Information Science

5. Some new terms : • Unresponsiveness. • Set decision • Mapping variable Haimonti Dutta, Department Of Computer and Information Science

6. What is an Influence Diagram ? A model for the domain U U D having a structural component probabilistic component Haimonti Dutta, Department Of Computer and Information Science

7. An Example f() b() ^ f ^b b f s ^s s(b,f) m m(s) ^m Haimonti Dutta, Department Of Computer and Information Science

8. Building an Influence diagram Steps involved : • Add a node to the diagram corresponding to each variable in U U D • Order the variables so that the unresponsiveness to D comes first. • For each Xi do Add a causal mechanism node Make Xi a deterministic function of Ci U Xi(Ci)where Ci is a causal mechanism node. Finally Assess the dependencies among the variables that are unresponsive D. Haimonti Dutta, Department Of Computer and Information Science

9. Influence diagrams in canonical forms Conditions : • Chance nodes descendents of D are decision nodes • Descendents of decision nodes are deterministic nodes Haimonti Dutta, Department Of Computer and Information Science

10. Learning Influence diagrams Observations : Information arcs and predecessors of a utility node are not learned We learn only the relevance arc structure and the physical probability We also know the states of all the decision variables and thus have a complete data for D in every case of the data base. Haimonti Dutta, Department Of Computer and Information Science

11. Hence… The problem of learning influence diagrams for the domain U U D reduces to Learning acausal bayesian networks for U UD where decision variables are interpreted as chance variables Haimonti Dutta, Department Of Computer and Information Science

12. Learning Causal Networks An example : Decision to quit smoking do we get lung cancer before sixty? x y Haimonti Dutta, Department Of Computer and Information Science

13. The problem : We cannot fully observe the mapping variable y(x) Haimonti Dutta, Department Of Computer and Information Science

14. Mechanism Components What are they? Haimonti Dutta, Department Of Computer and Information Science

15. Decomposition of the mapping variable y(x) y(x=0) y(x=1) x ŷ y Haimonti Dutta, Department Of Computer and Information Science

16. Component Independence Assumption that the mechanism components are independent. Y(x=1) y(x=0) x ŷ y Haimonti Dutta, Department Of Computer and Information Science

17. Another Problem The problem : Dependent Mechanisms A solution :Introduce additional domain variables in order to render mechanisms independent But…. We may not be able to observe the variables we introduce. Haimonti Dutta, Department Of Computer and Information Science

18. Learning in a causal network reduces to learning of acausal network when • Mechanism Independence • Component Independence and • Parameter Independence Haimonti Dutta, Department Of Computer and Information Science

19. Learning Causal Network structure We can use prior network methodology to establish priors for causal network learning provided the following holds: • Mechanism independence • Component independence • Parameter independence • Parameter modularity Haimonti Dutta, Department Of Computer and Information Science

20. Conclusion Some important points of focus : Mechanism Independence Component Independence Parameter Independence Parameter Modularity We use the above to learn causal networks from acausal networks Haimonti Dutta, Department Of Computer and Information Science