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 machine learning, the Markov blanket for a node A in a Bayesian network is the set of nodes \partial A composed of A'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 MB(A).

Every set of nodes in the network is conditionally independent of A when conditioned on the set \partial A, that is, when conditioned on the Markov blanket of the node A. The probability has the Markov property; formally, for distinct nodes A and B:

\Pr(A \mid \partial A , B) = \Pr(A \mid \partial A). \!

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. In a Markov random field, the Markov blanket for a node is simply its adjacent nodes.

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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.