# 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 ${\displaystyle A}$ in a Bayesian network is the set of nodes ${\displaystyle \partial A}$ composed of ${\displaystyle A}$'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. A Markov blanket may also be denoted by ${\displaystyle MB(A)}$.

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

${\displaystyle \Pr(A\mid \partial A,B)=\Pr(A\mid \partial A).\!}$

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 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.

## Notes

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.