1. General Gibbs Distribution
Representation
Probabilistic
Graphical
Models
Markov Networks
General Gibbs Distribution

2. A D B C

3. Consider a fully connected pairwise Markov network over X1,…,Xn where each Xi has d values. How many parameters does the network have?
O(dn)
O(nd)
O(n2d2)
O(nd)

5. Gibbs Distribution Parameters: a1 b1 c1 0.25 c2 0.35 b2 0.08 0.16 a2
0.05
0.07 a3
0.15
0.21
0.09
0.18
Parameters:

6. Gibbs Distribution

7. Induced Markov Network

8. Which Gibbs distribution corresponds to the graph H?
All of the above

9. Graph Structure & Factorization
Factorization not unique, but same independencies

10. Summary
Gibbs distribution represents distribution as a product of factors
Induced Markov network connects every pair of nodes that are in the same factor
Markov network structure doesn’t fully specify the factorization of P