1. Instructor: Prof. Pushpak Bhattacharyya 13/08/2004 CS-621/CS-449 Lecture Notes CS621/CS449 Artificial Intelligence Lecture Notes Set 7: 29/10/2004

2. Prof. Pushpak Bhattacharyya IIT Bombay 29/10/2004 CS-621/CS-449 Lecture Notes Outline Bayesian Belief Networks Example BBN

3. Prof. Pushpak Bhattacharyya IIT Bombay 29/10/2004 CS-621/CS-449 Lecture Notes 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.

4. Prof. Pushpak Bhattacharyya IIT Bombay 29/10/2004 CS-621/CS-449 Lecture Notes 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 : B A  C calls A : C A T F

5. Prof. Pushpak Bhattacharyya IIT Bombay 29/10/2004 CS-621/CS-449 Lecture Notes 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 X 1, X 2, … X m, then each row in the CPT records the values of X i s and the final column gives the value of P(Y| X 1, X 2, … X m ). For the Boolean case, the CPT of Y will have 2 m rows.

6. Prof. Pushpak Bhattacharyya IIT Bombay 29/10/2004 CS-621/CS-449 Lecture Notes 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

7. Prof. Pushpak Bhattacharyya IIT Bombay 29/10/2004 CS-621/CS-449 Lecture Notes Example BBN Topology P(B)P(~B) 0.60.4 P(E)P(~E) 0.0020.998 BEP(A)P(~A) TT0.950.05 TF0.940.06 FT0.20.8 FF0.0010.999 B E A BABA CACA AP(B A )P(~B A ) T1.00.0 F0.030.97 AP(C A )P(~C A ) T0.950.05 F0.01.0 positive mistakes