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CS621/CS449 Artificial Intelligence Lecture Notes Set 7: 29/10/2004 Instructor: Prof. Pushpak Bhattacharyya 13/08/2004 CS-621/CS-449 Lecture Notes Outline • Bayesian Belief Networks • Example BBN 29/10/2004 CS-621/CS-449 Lecture Notes Prof. Pushpak Bhattacharyya IIT Bombay Bayesian Belief Networks • BBNs : Data Structures for probabilistic inferencing • Example (from Russel & Norvik) A’s house has a burglar alarm. The alarm goes off when a burglar visits; but, it also goes off when an earthquake occurs. B & C are neighbours. B always calls A when the alarm goes off, but also calls A sometimes wrongly, when the doorbell rings. C sometimes misses calling A, since he cannot hear the alarm, his TV being too loud. 29/10/2004 CS-621/CS-449 Lecture Notes Prof. Pushpak Bhattacharyya IIT Bombay Random variables • We need to model the situation. • Note that B makes +ve mistakes and C makes –ve mistakes • Random variables (all Boolean variables) : T Burglar visit : B F Earthquake occurs : E Alarm goes off : A B calls A : BA C calls A : CA 29/10/2004 CS-621/CS-449 Lecture Notes Prof. Pushpak Bhattacharyya IIT Bombay Definition of BBN • A BBN is a DAG (Directed Acyclic Graph) where each node represents a random variable along with its CPT (Conditional Probability Table). An edge from X to Y depends on X. X is called the parent and Y is called the child. • CPT: If a node Y has parents X1, X2, … Xm, then each row in the CPT records the values of Xis and the final column gives the value of P(Y| X1, X2, … Xm). • For the Boolean case, the CPT of Y will have 2m rows. 29/10/2004 CS-621/CS-449 Lecture Notes Prof. Pushpak Bhattacharyya IIT Bombay Features of BBNs • Topology of BBN – captures dependencies • Models the most obvious dependencies, intuitively seen from the data. • Not all factors & events recorded. – Influences of these captured in CPT – Hidden nodes in BBNs • No edge b/w 2 nodes Independent events • CPT row sum = 1 29/10/2004 CS-621/CS-449 Lecture Notes Prof. Pushpak Bhattacharyya IIT Bombay Example BBN Topology P(B) 0.6 A T F 0.4 P(BA) 1.0 0.03 positive mistakes 29/10/2004 P(E) P(~B) E B P(~BA) 0.0 0.97 BA A CA P(~E) 0.002 0.998 B T T E T F P(A) 0.95 0.94 P(~A) 0.05 0.06 F F T F 0.2 0.001 0.8 0.999 A P(CA) P(~CA) T 0.95 F 0.0 CS-621/CS-449 Lecture Notes 0.05 1.0 Prof. Pushpak Bhattacharyya IIT Bombay