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

Bayesian Networks Data Model Directed Graphical Model Age 1.2 3.4 2.7 2.4 120 130 140 150 160 040 030 010 25 26 29 Salary Rate 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?

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

Gauging Modeling Efficacy == ? P S A R D P A R S D Age 1.2 3.4 2.7 2.4 120 130 140 150 160 040 030 010 25 26 29 Salary Rate Pmt 4 1 7 Delinquencies Data X1 X4 X3 X2 X5 Sample from “Gold Standard” network Compare performance with output from Structure Learner

Gauging Modeling Efficacy == ? Age 1.2 3.4 2.7 2.4 120 130 140 150 160 040 030 010 25 26 29 Salary Rate 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

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

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

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) )

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?

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

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

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

Ground Truth Causal Dependencies Data X1 X2 X3 X4 X5 Xnew Salary Rate Pmt Age Delinquencies New Var f(X1,X3,X5) 040 030 010 1.2 3.4 2.7 2.4 120 130 140 150 160 25 26 29 4 1 7 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

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

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

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

MBR

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

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

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

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

End http://www.quantumleap.us gfh@quantumleap.us Questions?