Graphical model: Difference between revisions

Revision as of 13:09, 30 April 2006

Revision as of 13:20, 30 April 2006

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In other words, the [[probability distribution|joint distribution]] factors into a product of conditional distributions. The graph structure indicates direct dependencies among random variables. Any two nodes that are not in a descendant/ancestor relationship are [[Conditional independence|conditionally independent]] given the values of their parents.

This type of graphical model is known as a directed graphical model, [[Bayesian network]], or belief network. Classic [[Machine learning|Machine learning]] methods like [[Hidden Markov Models|Hidden Markov Models]] or [[Neural networks|Neural networks]] can be considered as special cases of Bayesian networks.

There are also undirected graphical models, generally called [[Markov random fields|Markov random fields]].

Classic [[Machine learning|Machine learning]] methods like [[Hidden Markov Models|Hidden Markov Models]] or [[Neural networks|Neural networks]] can be considered as special cases of graphical models.

Applications of graphical models include modelling of [[gene regulatory network]]s, speech recognition, gene finding, computer vision and the diagnosis of diseases.

There are also undirected graphical models, also called [[Markov network|Markov networks]], in which graph separation encodes conditional independencies (these are also known as graphical Gaussian models, or GGMs).

A good reference for learning the basics of graphical models is written by Neapolitan, Learning Bayesian networks (2004). A more advanced and more statistically oriented book is by Cowell, Dawid, Lauritzen and Spiegelhalter, GraphicalProbabilistic modelsnetworks and expert systems (19961999). See also [[belief propagation]].

A recent application of graphical models is to describe [[gene regulatory network]]s.

See also [[belief propagation]].

A good reference for learning the basics of graphical models is written by Neapolitan, Learning Bayesian networks (2004). A more advanced and more statistically oriented book is by Lauritzen, Graphical models (1996).

[[Category:probability theory]]