Graphical model: Difference between revisions

Revision as of 04:58, 15 April 2025

Revision as of 22:20, 24 July 2025

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===Undirected Graphical Model===

[[File:Examples of an Undirected Graph.svg|thumb|alt=An undirected graph with four vertices.|An undirected graph with four vertices.]]

The undirected graph shown may have one of several interpretations; the common feature is that the presence of an edge implies some sort of dependence between the corresponding random variables. From this graph, we might deduce that B, C, and D are all [[Conditional independence|conditionally independent]] given A. This means that if the value of A is known, then the values of B, C, and D provide no further information about each other. Equivalently (in this case), the joint probability distribution can be factorized as:

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{{main|Bayesian network}}

[[File:Example of a Directed Graph.svg|thumb|alt=Example of a directed acyclic graph on four vertices.|Example of a directed acyclic graph on four vertices.]]

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*[[Dependency network (graphical model)|Dependency network]] where cycles are allowed

*Tree-augmented classifier or '''TAN model'''

[[File:Tan corral.png|thumb| TAN model for "corral dataset".]]

*Targeted Bayesian network learning (TBNL) [[File:Tbnl corral.jpg|thumb|TBNL model for "corral dataset"]]

*A [[factor graph]] is an undirected [[bipartite graph]] connecting variables and factors. Each factor represents a function over the variables it is connected to. This is a helpful representation for understanding and implementing [[belief propagation]].