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Markov Networks

Markov Networks. Markov Networks. Smoking. Cancer. Undirected graphical models. Asthma. Cough. Potential functions defined over cliques. Markov Networks. Smoking. Cancer. Undirected graphical models. Asthma. Cough. Log-linear model:. Weight of Feature i. Feature i.

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Markov Networks

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  1. Markov Networks

  2. Markov Networks Smoking Cancer • Undirected graphical models Asthma Cough • Potential functions defined over cliques

  3. Markov Networks Smoking Cancer • Undirected graphical models Asthma Cough • Log-linear model: Weight of Feature i Feature i

  4. 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”)

  5. Markov Nets vs. Bayes Nets

  6. Moralization To convert a Bayesian network into a Markov network: • For each variable:Add arcs between its parents(“marry” them) • Remove arrows

  7. Examples • Statistical physics • Vision / Image processing • Social networks • Web page classification • Etc.

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