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

2. 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

3. 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

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

5. 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

6. 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

7. 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

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

11. 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

12. 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

13. 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

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

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

17. 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

18. 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

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

20. 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