Markov blanket

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In a Bayesian network, Markov blanket of node A includes its parents, children and the other parents of all of its children.
In a Bayesian network, 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 MB(A) composed of A's parents, its children, and its children's parents. In a Markov network, the Markov blanket of a node is its set of neighbouring nodes.

Every node in the network is conditionally independent of A when conditioned on the set MB(A), that is, when conditioned on the Markov blanket of the node A. Formally, for distinct nodes A and B:

\Pr(A \mid \mathit{MB}(A) \cap B) = \Pr(A \mid \mathit{MB}(A)). \!

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.

The Markov blanket of a node is interesting because it identifies all the variables that shield off the node from the rest of the network. This means that the Markov blanket of a node is the only knowledge that is needed to predict the behaviour of that node.

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