Markov blanket

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In a Bayesian network, the Markov blanket of node A includes its parents, children and the other parents of all of its children.

In statistics and machine learning, the Markov blanket for a node in a graphical model 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 and its children. The term was coined by Judea 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. In a Markov random field, the Markov blanket for a node is simply its adjacent nodes.

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 random field, the Markov blanket of a node is its set of neighboring nodes. The Markov blanket of A 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 :

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  1. ^ Pearl, Judea (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Representation and Reasoning Series. San Mateo CA: Morgan Kaufmann. ISBN 0-934613-73-7.