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Markov Networks

Explore the realm of Markov Networks bridging Smoking, Cancer, Asthma, Cough, and more. Learn about undirected graphical models, log-linear models, and the Hammersley-Clifford Theorem. Discover the distinctions between Markov Networks and Bayes Nets, and understand the process of moralization in network transformation. Examples in statistical physics, vision processing, social networks, web classification, and more await your exploration.

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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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