- Graphical model
In

probability theory ,statistics , andmachine learning , a**graphical model (GM)**is a graph that represents independencies amongrandom variable s by a graph in which each node is a random variable, and the missing edges between the nodes represent conditional independencies.Two common types of GMs correspond to graphs with directed and undirected edges. If the network structure of the model is a

directed acyclic graph (DAG), the GM represents a factorization of the jointprobability of all random variables. More precisely, if the events are:"X"

_{1}, ..., "X"_{"n"},then the joint probability

:"P"("X"

_{1}, ..., "X"_{"n"}),is equal to the product of the conditional probabilities

:P("X

_{i}" | parents of "X_{i}") for "i" = 1,...,"n".In other words, the

joint distribution factors into a product of conditional distributions. Any two nodes that are not connected by an arrow are conditionally independent given the values of their parents. In general, any two sets of nodes are conditionallyindependent given a third set if a criterion called "d"-separation holds in the graph. It will turn out that the local independencies and global independecies are equivalent in Bayesian networks.This type of graphical model is known as a directed graphical model,

Bayesian network , or belief network. Classic machine learning models likehidden Markov models ,neural networks and newer models such asvariable-order Markov model s can be considered as special cases of Bayesian networks.Graphical models with undirected edges are generally called

Markov random field s orMarkov network s. A graphical model with many repeated subunits can be represented withplate notation .A third type of graphical model is a

factor graph , which is an undirectedbipartite graph connecting variables and "factor nodes". Each factor represents a probability distribution over the variables it is connected to. In contrast to a Bayesian network, a factor may be connected to more than two nodes.Applications of graphical models include

speech recognition ,computer vision , decoding oflow-density parity-check codes , modeling ofgene regulatory network s, gene finding and diagnosis of diseases.A good reference for learning the basics of graphical models is written by Neapolitan, "Learning Bayesian networks" (2004) and another is Finn Verner Jensen's "An Introduction to Bayesian Networks" from 1996. [

*Cite book*] A more advanced and statistically oriented book is by Cowell, Dawid, Lauritzen and Spiegelhalter, "Probabilistic networks and expert systems" (1999).

author =Finn Verner Jensen

title = An Introduction to Bayesian Networks

year = 1996

publisher =Springer Verlag

location = New York

isbn = 0387915028A computational reasoning approach is provided in

Judea Pearl 's "Probabilistic Reasoning in Intelligent Systems" from 1988Cite book

author =Judea Pearl

year = 1988

title = Probabilistic Reasoning in Intelligent Systems

edition = Revised Second Printing

location = San Mateo, CA

publisher =Morgan Kaufmann ] where the relationships between graphs andprobabilities were formally introduced.**ee also***

Markov network

*Bayesian network

*Belief propagation

*Structural equation model **References****Others*** [

*http://research.microsoft.com/%7Ecmbishop/PRML/Bishop-PRML-sample.pdf Graphical models, Chapter 8 of Pattern Recognition and Machine Learning by Christopher M. Bishop*]

* [*http://www.cs.ubc.ca/~murphyk/Bayes/bnintro.html A Brief Introduction to Graphical Models and Bayesian Networks*]

* [ftp://ftp.research.microsoft.com/pub/tr/tr-95-06.pdf Heckerman's Bayes Net Learning Tutorial]

* Cite journal

author =Edoardo M. Airoldi

title = Getting Started in Probabilistic Graphical Models

journal =PLoS Computational Biology

volume = 3

issue = 12

pages = e252

year = 2007

doi = 10.1371/journal.pcbi.0030252

url = http://compbiol.plosjournals.org/perlserv/?request=get-document&doi=10.1371/journal.pcbi.0030252&ct=1

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