Graphical model: Difference between revisions

Revision as of 23:24, 16 October 2006

Revision as of 02:21, 18 October 2006

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In [[probability theory]] and [[statistics]], a '''graphical model (GM)''' represents [[statistical independence|dependencies]] among [[random variable|random variables]]s by a [[graph (mathematics)|graph]] in which each random variable is a node, and the edges between the nodes represent conditional dependencies.

In the simplest case, the network structure of the model is a [[directed acyclic graph]] (DAG). Then the GM represents a factorization of the joint [[probability]] of all random variables. More precisely, if the events are

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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.

Graphical models with undirected edges are generally called [[Markov random fields|Markov random fields]] or [[Markov networks|Markov networks]].

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

A good reference for learning the basics of graphical models is written by Neapolitan, Learning Bayesian networks (2004). A more advanced and statistically oriented book is by Cowell, Dawid, Lauritzen and Spiegelhalter, Probabilistic networks and expert systems (1999). See also [[belief propagation]].

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[[Category:Bayesian networks]]

[[Category:Statistics]]

[[es:Modelo en grafo]]