A Bayesian Approach to Learning Causal networks David Heckerman 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science

Haimonti Dutta, Department Of Computer and Information Science 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 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science

Haimonti Dutta, Department Of Computer and Information Science 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. 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science

Causal Bayesian Networks and Influence diagrams A Causal Network : b f m s 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science

Haimonti Dutta, Department Of Computer and Information Science Some new terms : Unresponsiveness. Set decision Mapping variable 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science

What is an Influence Diagram ? A model for the domain U U D having a structural component probabilistic component 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science

Haimonti Dutta, Department Of Computer and Information Science An Example f() b() ^ f ^b b f s ^s s(b,f) m m(s) ^m 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science

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. 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science

Influence diagrams in canonical forms Conditions : Chance nodes descendents of D are decision nodes Descendents of decision nodes are deterministic nodes 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science

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. 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science

Haimonti Dutta, Department Of Computer and Information Science 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 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science

Learning Causal Networks An example : Decision to quit smoking do we get lung cancer before sixty? x y 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science

Haimonti Dutta, Department Of Computer and Information Science The problem : We cannot fully observe the mapping variable y(x) 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science

Haimonti Dutta, Department Of Computer and Information Science Mechanism Components What are they? 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science

Decomposition of the mapping variable y(x) ŷ y 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science

Component Independence Assumption that the mechanism components are independent. Y(x=1) y(x=0) x ŷ y 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science

Haimonti Dutta, Department Of Computer and Information Science 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. 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science

Haimonti Dutta, Department Of Computer and Information Science Learning in a causal network reduces to learning of acausal network when Mechanism Independence Component Independence and Parameter Independence 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science

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 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science

Haimonti Dutta, Department Of Computer and Information Science 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 11/22/2018 Haimonti Dutta, Department Of Computer and Information Science