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Properties of BP Algorithm

Inference. Probabilistic Graphical Models. Message Passing. Properties of BP Algorithm. Calibration. Cluster beliefs: A cluster graph is calibrated if every pair of adjacent clusters C i , C j agree on their sepset S i,j. 1: A,B. 4: A,D. A. B. D. 2: B,C. 3: C,D. C.

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Properties of BP Algorithm

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  1. 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,Cjagree on their sepsetSi,j 1: A,B 4: A,D A B D 2: B,C 3: C,D C

  3. Convergence  Calibration • Convergence:

  4. Reparameterization • Sepsetmarginals: 1: A,B 4: A,D A B D 2: B,C 3: C,D C

  5. Reparameterization • Sepsetmarginals:

  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

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