2007 PracticalStatisticalAI

Subject Headings: Statistical Relational Model, Markov Network

Quotes

Plan

• We have the elements:
• Probability for handling uncertainty
• Logic for representing types, relations, and complex dependencies between them
• Learning and inference algorithms for each

Hammersley-Clifford Theorem

• If Distribution is strictly positive (P(x) > 0)
• And Graph encodes conditional independences
• Then Distribution is product of potentials over cliques of graph
• Inverse is also true.

(“Markov network = Gibbs distribution”

Markov Nets vs. Bayes Nets

| Property | Markov Nets | Bayes Nets| | Form | Prod. potentials | Prod. potentials| | Potentials | Arbitrary | Cond. probabilities| | Cycles | Allowed | Forbidden| | Partition func. | Z = ? | Z = 1| | Indep. check | Graph separation | D-separation| | Indep. props. | Some | Some| | Inference | MCMC, BP, etc. | Convert to Markov|

References

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volumeDate ValuetitletypejournaltitleUrldoinoteyear
2007 PracticalStatisticalAIPractical Statistical Relational AIhttp://www.cs.washington.edu/homes/pedrod/psrl.ppt