1. A Direct Measure for the Efficacy of Bayesian Network Structures Learned from Data
Gary F. Holness

2. Bayesian Networks Data Model Directed Graphical Model
Age
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2.4
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010 25 26 29
Salary
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Pmt 4 1 7
Delinquencies
Data X1 X4 X3 X2 X5 P A R S D
Model X2 X4 X1 X3 X5
Directed Graphical Model
Compact encoding of joint probability
Product of conditionally independent factors
Makes inference more tractable
Here structure is given, how to learn it?

3. Structure Learning in Bayesian Networks
connectivity 1 P A R S D P A R S D
score( )
> score( ) P A R S D P A R S D
causal ordering A R S P D
Begin with representation: connectivity and edge directedness
Search large state space of model definitions
Select the best structure

4. Gauging Modeling Efficacy== ? P S A R D P A R S D
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2.4
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Data X1 X4 X3 X2 X5
Sample from “Gold Standard” network
Compare performance with output from Structure Learner

5. Gauging Modeling Efficacy== ?
Age
1.2
3.4
2.7
2.4
120
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140
150
160
040
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010 25 26 29
Salary
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Pmt 4 1 7
Delinquencies
Data X1 X4 X3 X2 X5
Gold Standard P S A R D
Does the Gold standard modeling true causal dependencies
Discounts good models

6. Topics
Introduction
Markov Blanket
Ground Truth Causal Dependence
Markov Blanket Retrieval
Results and Future Consideration

7. Topics
Introduction
Markov Blanket
Ground Truth Causal Dependence
Markov Blanket Retrieval
Results and Future Consideration

8. Markov Blanket G = (V,E) V = {A, B, C, …, Z} E V x V
MB(A) = parents(A) U children(A) U spouses(A)
A is d-separated from remaining nodes R= V–MB(A)–A, given MB(A)
P(A | MB(A), R) = P(A | MB(A) )

9. Markov Blanket G = (V,E) V = {A, B, C, …, Z} E V x V
Markov Blankets define the probability distribution
Modeling Efficacy  captures true influences
Are the Markov Blankets correct?

10. Topics
Introduction
Markov Blanket
Ground Truth Causal Dependence
Markov Blanket Retrieval
Results and Future Consideration

11. Topics
Introduction
Markov Blanket
Ground Truth Causal Dependence
Markov Blanket Retrieval
Results and Future Consideration

12. Ground Truth Causal Dependencies? ? ? ? ? ?
How do you know the true influences?
Not so easy for real-world data

13. Ground Truth Causal Dependencies
Data X1 X2 X3 X4 X5
Xnew
Salary
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Pmt
Age
Delinquencies
New Var
f(X1,X3,X5)
040
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f(X1,X3,X5)
Xnew X1 X5 X3
f(X1,X3,X5)
f(X1,X3,X5)
f(X1,X3,X5)
How do you know the true influences?
You create them

14. Topics
Introduction
Markov Blanket
Ground Truth Causal Dependence
Markov Blanket Retrieval
Results and Future Consideration

15. Topics
Introduction
Markov Blanket
Ground Truth Causal Dependence
Markov Blanket Retrieval
Results and Future Consideration

16. Markov Blanket Retrieval (MBR)
Markov Blankets from Structure Learning
Ground Truth Markov Blanket
Xnew X1 X2 X3
search
query
collection
Treat ground truth as query
Treat learned structures as collection of Markov Blankets
Search collection for ground truth document

17. MBR

18. Topics
Introduction
Markov Blanket
Ground Truth Causal Dependence
Markov Blanket Retrieval
Results and Future Consideration

19. Topics
Introduction
Markov Blanket
Ground Truth Causal Dependence
Markov Blanket Retrieval
Results and Future Consideration

20. Results K2GA structure learner vary population and generations
discrete, continuous, and mixed data-sets

21. Further Considerations
Measure the effect of MB-variable correlations
Causal relationships beyond MB-membership
Sensitivity to causal strength

22. End
Questions?