Graphical Models

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Graphical Models
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Intro

• Models with modest variables run into
  computation problems.
• What queries are we interested in
• (in) dependencies and condional marginal
  probabilities.
• A marriage between graph theory and probability
  theory will
• provide the language for this structure.
• two flavors directed undirected graphical
  models.
• independencies implied by graph ? structures
  prob. distr.

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Directed Acyclic Graphs

• prob. distr. prod. of local factors
• no cycles allowed!
• structure Bayes rule, with some dependencies
  removed
• interpretation causal depencies between parents
  children
• d-separability.
• 3 canonical subgraphs ? Bayes ball algorithm

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Undirected Graphs

• Graph separability ? undirected graphs
• prob. distr. prod of un-normalized factors
• factors live on maximal cliques
• there are UGM that imply cond. indep. not
  captures in any DGM, and vice versa.
• simplified parametrizations for computational
  efficiency.