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Understanding Markov Networks and Log-Linear Models for Pattern Recognition

Explore Markov Networks, log-linear models, and their applications in fields such as statistical physics, image processing, and social networks. Learn about the relationship between Markov Networks and Bayes Nets, potential functions defined over cliques, and the Hammersley-Clifford Theorem.

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Understanding Markov Networks and Log-Linear Models for Pattern Recognition

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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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