1. Pairwise Markov Networks
Representation
Probabilistic
Graphical
Models
Markov Networks
Pairwise Markov Networks

2. Alice
Debbie
Bob
Charles

3. A D B C

4. B D C A

5. Consider the pairwise factor 1(A,B)
Consider the pairwise factor 1(A,B). That potential is proportional to:
The marginal probability P(A,B)
The conditional probability P(A | B)
The conditional probability P(A, B | C, D)
None of the above

6. B D C A A B
Prob. a0 b0
0.13 b1
0.69 a1
0.14
0.04

7. Pairwise Markov Networks
A pairwise Markov network is an undirected graph whose nodes are X1,…,Xn
and each edge Xi―Xj is associated with a factor (potential) ij(Xi―Xj)

8. A1,1
A1,2
A1,3
A1,4
A2,1
A2,2
A2,3
A2,4
A3,1
A3,2
A3,3
A3,4
A4,1
A4,2
A4,3
A4,4

10. (a)
(b)
(c)
(d)

11. END END END