Graphical Models.

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Presentation transcript:

Graphical Models

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.

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

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.