CS621/CS449 Artificial Intelligence Lecture Notes

1. CS621/CS449Artificial IntelligenceLecture Notes Set 7: 29/10/2004 CS-621/CS-449 Lecture Notes

2. Outline • Bayesian Belief Networks • Example BBN CS-621/CS-449 Lecture Notes

3. 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. CS-621/CS-449 Lecture Notes

4. Random variables • We need to model the situation. • Note that B makes +ve mistakes and C makes –ve mistakes • Random variables (all Boolean variables) : • Burglar visit : B • Earthquake occurs : E • Alarm goes off : A • B calls A : BA • C calls A : CA T F CS-621/CS-449 Lecture Notes

5. 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. CS-621/CS-449 Lecture Notes

6. 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 CS-621/CS-449 Lecture Notes

7. Example BBN Topology E B A BA CA positive mistakes CS-621/CS-449 Lecture Notes