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[[Image:Diagram of a Markov blanket.svg|frame|In a Bayesian network, the Markov blanket of node ''A'' includes its parents, children and the other parents of all of its children.]] | |||
In [[machine learning]], the '''Markov blanket''' for a [[Vertex (graph theory)|node]] <math>A</math> in a [[Bayesian network]] is the set of nodes <math>\partial A</math> composed of <math>A</math>'s parents, its children, and its children's other parents. In a [[Markov network]], the Markov blanket of a node is its set of neighboring nodes. A Markov blanket may also be denoted by <math>MB(A)</math>. | |||
Every set of nodes in the network is [[conditional independence|conditionally independent]] of <math>A</math> when conditioned on the set <math>\partial A</math>, that is, when conditioned on the Markov blanket of the node <math>A</math>. The probability has the [[Markov property]]; formally, for distinct nodes <math>A</math> and <math>B</math>: | |||
:<math>\Pr(A \mid \partial A , B) = \Pr(A \mid \partial A). \!</math> | |||
The Markov blanket of a node contains all the variables that shield the node from the rest of the network. This means that the Markov blanket of a node is the only knowledge needed to predict the behavior of that node. The term was coined by [[Judea Pearl| Pearl]] in 1988.<ref>{{cite book |last=Pearl |first=Judea |authorlink=Judea Pearl |title=Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference |publisher=Morgan Kaufmann |location=San Mateo CA |year=1988 |isbn=0-934613-73-7 | series=Representation and Reasoning Series}}</ref> | |||
In a Bayesian network, the values of the parents and children of a node evidently give information about that node; however, its children's parents also have to be included, because they can be used to explain away the node in question. | |||
== See also == | |||
* [[Moral graph]] | |||
==Notes== | |||
<references/> | |||
[[Category:Probability theory]] | |||
[[Category:Bayesian networks]] | |||
[[Category:Markov networks]] | |||
Revision as of 03:41, 28 October 2013
In machine learning, the Markov blanket for a node in a Bayesian network is the set of nodes composed of 's parents, its children, and its children's other parents. In a Markov network, the Markov blanket of a node is its set of neighboring nodes. A Markov blanket may also be denoted by .
Every set of nodes in the network is conditionally independent of when conditioned on the set , that is, when conditioned on the Markov blanket of the node . The probability has the Markov property; formally, for distinct nodes and :
The Markov blanket of a node contains all the variables that shield the node from the rest of the network. This means that the Markov blanket of a node is the only knowledge needed to predict the behavior of that node. The term was coined by Pearl in 1988.[1]
In a Bayesian network, the values of the parents and children of a node evidently give information about that node; however, its children's parents also have to be included, because they can be used to explain away the node in question.
See also
Notes
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