1. Properties of BP Algorithm
Inference
Probabilistic
Graphical
Models
Message Passing
Properties of BP Algorithm

2. Calibration Cluster beliefs:
A cluster graph is calibrated if every pair of adjacent clusters Ci,Cj agree on their sepset Si,j
2: B,C
1: A,B
3: C,D
4: A,D C A B D

3. Convergence  Calibration

4. Reparameterization Sepset marginals: 2: B,C 1: A,B 3: C,D 4: A,D C A B

5. Reparameterization
Sepset marginals:

6. Summary At convergence of BP, cluster graph beliefs are calibrated:
beliefs at adjacent clusters agree on sepsets
Cluster graph beliefs are an alternative, calibrated parameterization of the original unnormalized density
No information is lost by message passing

7. END END END